diff --git a/s3fs/core.py b/s3fs/core.py
index 80b6fe95..2843b918 100644
--- a/s3fs/core.py
+++ b/s3fs/core.py
@@ -1019,12 +1019,17 @@ async def _exists(self, path):
                     "list_objects_v2", MaxKeys=1, Bucket=bucket, **self.req_kw
                 )
                 return True
-            except Exception:
+            except (FileNotFoundError, PermissionError):
                 pass
             try:
                 await self._call_s3("get_bucket_location", Bucket=bucket, **self.req_kw)
                 return True
-            except Exception:
+            except FileNotFoundError:
+                return False
+            except PermissionError:
+                logger.warning(
+                    "Bucket %s doesn't exist or you don't have access to it.", bucket
+                )
                 return False
 
     exists = sync_wrapper(_exists)
diff --git a/s3fs/tests/test_s3fs.py b/s3fs/tests/test_s3fs.py
index 1b4cd769..88def234 100644
--- a/s3fs/tests/test_s3fs.py
+++ b/s3fs/tests/test_s3fs.py
@@ -21,6 +21,7 @@
 from s3fs.core import S3FileSystem
 from s3fs.utils import ignoring, SSEParams
 from botocore.exceptions import NoCredentialsError
+from botocore.exceptions import EndpointConnectionError
 from fsspec.asyn import sync
 from fsspec.callbacks import Callback
 from packaging import version
@@ -2464,6 +2465,40 @@ def test_exists_isdir(s3):
     assert not s3.isdir(bad_path)
 
 
+def test_exists_raises_on_connection_error():
+    # Ensure that we raise a ConnectionError instead of returning False if we
+    # are not actually able to connect to storage, by setting a fake proxy and
+    # then re-creating the S3FileSystem instance.
+    S3FileSystem.clear_instance_cache()
+    s3 = S3FileSystem(
+        anon=False,
+        skip_instance_cache=True,
+        endpoint_url="https://fakeproxy.127.0.0.1:8080/",
+    )
+    s3.invalidate_cache()
+    with pytest.raises(EndpointConnectionError):
+        s3.exists("this-bucket-does-not-exist/")
+
+
+def test_exists_bucket_nonexistent_or_no_access(caplog):
+    # Ensure that a warning is raised and False is returned if querying a
+    # bucket that might either not exist or be private.
+    # This tests against real AWS, might fail due to network issues.
+    caplog.clear()
+    fs = s3fs.S3FileSystem(key="wrongkey", secret="wrongsecret")
+    assert not fs.exists("s3://this-bucket-might-not-exist/")
+    assert caplog.records[0].levelname == "WARNING"
+    assert "doesn't exist or you don't have access" in caplog.text
+
+
+def test_exists_bucket_nonexistent(s3, caplog):
+    # Ensure that NO warning is raised and False is returned if checking bucket
+    # existance when we have full access.
+    caplog.clear()
+    assert not s3.exists("non_existent_bucket/")
+    assert len(caplog.records) == 0
+
+
 def test_list_del_multipart(s3):
     path = test_bucket_name + "/afile"
     f = s3.open(path, "wb")