I think it's probably ok not to trust it right now, but give him a chance to prove it or prove otherwise...
I actually met H about a year before B, so I don't have any good advice there. We also all went "in" to this relationship at the same time, even though there was some different intentions at the beginning. Maybe try to think of meeting her like anyone else you meet. It'll get more "normal" to you the more you're around it.