diff --git a/jira/client.py b/jira/client.py
index 36dc2fea9..c33fda876 100644
--- a/jira/client.py
+++ b/jira/client.py
@@ -307,30 +307,24 @@ def _sort_and_quote_values(self, values):
         return [quote(value, safe="~") for value in ordered_values]
 
 
-class JiraCookieAuth(AuthBase):
-    """Jira Cookie Authentication.
-
-    Allows using cookie authentication as described by `jira api docs <https://developer.atlassian.com/server/jira/platform/cookie-based-authentication/>`_
-    """
+class RetryingJiraAuth(AuthBase):
+    """Base class for Jira authentication handlers that need to retry requests on 401 responses."""
 
-    def __init__(
-        self, session: ResilientSession, session_api_url: str, auth: tuple[str, str]
-    ):
-        """Cookie Based Authentication.
-
-        Args:
-            session (ResilientSession): The Session object to communicate with the API.
-            session_api_url (str): The session api url to use.
-            auth (Tuple[str, str]): The username, password tuple.
-        """
+    def __init__(self, session: ResilientSession | None = None):
         self._session = session
-        self._session_api_url = session_api_url  # e.g ."/rest/auth/1/session"
-        self.__auth = auth
         self._retry_counter_401 = 0
         self._max_allowed_401_retries = 1  # 401 aren't recoverable with retries really
 
+    def init_session(self):
+        """Auth mechanism specific code to re-initialize the Jira session."""
+        raise NotImplementedError()
+
     @property
     def cookies(self):
+        """Return the cookies from the session."""
+        assert (
+            self._session is not None
+        )  # handle_401 should've caught this before attempting retry
         return self._session.cookies
 
     def _increment_401_retry_counter(self):
@@ -339,22 +333,6 @@ def _increment_401_retry_counter(self):
     def _reset_401_retry_counter(self):
         self._retry_counter_401 = 0
 
-    def __call__(self, request: requests.PreparedRequest):
-        request.register_hook("response", self.handle_401)
-        return request
-
-    def init_session(self):
-        """Initialise the Session object's cookies, so we can use the session cookie.
-
-        Raises HTTPError if the post returns an erroring http response
-        """
-        username, password = self.__auth
-        authentication_data = {"username": username, "password": password}
-        r = self._session.post(  # this also goes through the handle_401() hook
-            self._session_api_url, data=json.dumps(authentication_data)
-        )
-        r.raise_for_status()
-
     def handle_401(self, response: requests.Response, **kwargs) -> requests.Response:
         """Refresh cookies if the session cookie has expired. Then retry the request.
 
@@ -364,14 +342,19 @@ def handle_401(self, response: requests.Response, **kwargs) -> requests.Response
         Returns:
             requests.Response
         """
-        if (
+        is_retryable_401 = (
             response.status_code == 401
             and self._retry_counter_401 < self._max_allowed_401_retries
-        ):
+        )
+
+        if is_retryable_401 and self._session is not None:
             LOG.info("Trying to refresh the cookie auth session...")
             self._increment_401_retry_counter()
             self.init_session()
             response = self.process_original_request(response.request.copy())
+        elif is_retryable_401 and self._session is None:
+            LOG.warning("No session was passed to constructor, can't refresh cookies.")
+
         self._reset_401_retry_counter()
         return response
 
@@ -379,21 +362,67 @@ def process_original_request(self, original_request: requests.PreparedRequest):
         self.update_cookies(original_request)
         return self.send_request(original_request)
 
+    def update_cookies(self, original_request: requests.PreparedRequest):
+        """Auth mechanism specific cookie handling prior to retrying."""
+        raise NotImplementedError()
+
+    def send_request(self, request: requests.PreparedRequest):
+        if self._session is not None:
+            request.prepare_cookies(self.cookies)  # post-update re-prepare
+            return self._session.send(request)
+
+
+class JiraCookieAuth(RetryingJiraAuth):
+    """Jira Cookie Authentication.
+
+    Allows using cookie authentication as described by `jira api docs <https://developer.atlassian.com/server/jira/platform/cookie-based-authentication/>`_
+    """
+
+    def __init__(
+        self, session: ResilientSession, session_api_url: str, auth: tuple[str, str]
+    ):
+        """Cookie Based Authentication.
+
+        Args:
+            session (ResilientSession): The Session object to communicate with the API.
+            session_api_url (str): The session api url to use.
+            auth (Tuple[str, str]): The username, password tuple.
+        """
+        super().__init__(session)
+        self._session_api_url = session_api_url  # e.g ."/rest/auth/1/session"
+        self.__auth = auth
+
+    def __call__(self, request: requests.PreparedRequest):
+        request.register_hook("response", self.handle_401)
+        return request
+
+    def init_session(self):
+        """Initialise the Session object's cookies, so we can use the session cookie.
+
+        Raises HTTPError if the post returns an erroring http response
+        """
+        assert (
+            self._session is not None
+        )  # Constructor for this subclass always takes a session
+        username, password = self.__auth
+        authentication_data = {"username": username, "password": password}
+        r = self._session.post(  # this also goes through the handle_401() hook
+            self._session_api_url, data=json.dumps(authentication_data)
+        )
+        r.raise_for_status()
+
     def update_cookies(self, original_request: requests.PreparedRequest):
         # Cookie header needs first to be deleted for the header to be updated using the
         # prepare_cookies method. See request.PrepareRequest.prepare_cookies
         if "Cookie" in original_request.headers:
             del original_request.headers["Cookie"]
-        original_request.prepare_cookies(self.cookies)
-
-    def send_request(self, request: requests.PreparedRequest):
-        return self._session.send(request)
 
 
-class TokenAuth(AuthBase):
+class TokenAuth(RetryingJiraAuth):
     """Bearer Token Authentication."""
 
-    def __init__(self, token: str):
+    def __init__(self, token: str, session: ResilientSession | None = None):
+        super().__init__(session)
         # setup any auth-related data here
         self._token = token
 
@@ -402,6 +431,15 @@ def __call__(self, r: requests.PreparedRequest):
         r.headers["authorization"] = f"Bearer {self._token}"
         return r
 
+    def init_session(self):
+        pass  # token should still work, only thing needed is to clear session cookies which happens next
+
+    def update_cookies(self, _):
+        assert (
+            self._session is not None
+        )  # handle_401 on the superclass should've caught this before attempting retry
+        self._session.cookies.clear_session_cookies()
+
 
 class JIRA:
     """User interface to Jira.
@@ -4306,7 +4344,7 @@ def _create_token_session(self, token_auth: str):
 
         Header structure: "authorization": "Bearer <token_auth>".
         """
-        self._session.auth = TokenAuth(token_auth)
+        self._session.auth = TokenAuth(token_auth, session=self._session)
 
     def _set_avatar(self, params, url, avatar):
         data = {"id": avatar}