No known relation between the two. Only noting how they altered the course of one-party control in each of their states with respect to a Senate seat (which in both cases took three terms to regain control again).
When you mentioned another Bass serving in Congress at the same time in another state, I immediately assumed it must have been a case of the family dynasty exporting their clan to other states. Instead, it just sounds like the case of powerful political RAT family Richard E. Byrd, Harry F. Byrd & Harry F. Byrd Jr. in Virginia and the unrelated but almost identically named and similarly powerful RAT Senator Robert C. Byrd in West Virginia.