diff --git a/google/cloud/storage/blob.py b/google/cloud/storage/blob.py
index b1e13788d..301671aec 100644
--- a/google/cloud/storage/blob.py
+++ b/google/cloud/storage/blob.py
@@ -1611,7 +1611,8 @@ def _do_multipart_upload(
         headers, object_metadata, content_type = info
 
         base_url = _MULTIPART_URL_TEMPLATE.format(
-            hostname=self.client._connection.API_BASE_URL, bucket_path=self.bucket.path
+            hostname=self._require_client(client)._connection.API_BASE_URL,
+            bucket_path=self.bucket.path
         )
         name_value_pairs = []
 
@@ -1780,7 +1781,8 @@ def _initiate_resumable_upload(
             headers.update(extra_headers)
 
         base_url = _RESUMABLE_URL_TEMPLATE.format(
-            hostname=self.client._connection.API_BASE_URL, bucket_path=self.bucket.path
+            hostname=self._require_client(client)._connection.API_BASE_URL,
+            bucket_path=self.bucket.path
         )
         name_value_pairs = []