Okay, so to be clear, "SSL Bridging" generally defines where the F5 both decrypts and re-encrypts the traffic to the server, which requires both client and server SSL profiles. If I can assume that there is NO client certificate auth going on, on either side, then the "certificate unknown" error is going to come from the client after consuming the server's certificate.
Browsers aren't usually that strict about bad server certificates. Worst case you'll get a certificate warning and click-to-continue.
So then I'd ask,
- Does the app server require HTTPS?
- Do you have a server SSL profile also applied?
- And if yes to the above, which server SSL profile are you using?