You can report them if the trash talk gets too serious, or you can disable chat. Though there are many who are pleasant to chat to I wouldn't say bullet chess is conducive to chatting. As far as chat after the game, you can just ignore most things and move on, or like I said report if necessary. I'd like to think the majority of people will NOT call you names.
I do find that there are not a very large amount of people who enjoy rematches but this could be for a number of reasons.
I always get random trash talker in chat while I'm playing this site at rating 1200-1500+, why I won't accept rematch offer because people always run after 1 rematch and then call me noob or whatever.
then when they see me again they will abort, but btw I love people on this site.