which Persistence to use when F5 works in SSL Bridging mode and traffic is natted at core.

Are you terminating SSL with a client-ssl profile then re-encrypting with a server-ssl profile? If you do that you should be able to use an HTTP profile and cookie persistence. The default "insert cookie" method is the easiest cookie method to use and should work just fine for you. Remember you can't use cookie persistence without an HTTP profile. I would also highly recommend using a OneConnect profile with cookie persistence or else you run the risk on not load balancing all requests to the same server.