if you are doing bbfs do you worry you will get hit with a paternity suit?

I wouldn't do BBFS.

Back when I often didn't have a good sense of what type of hooker I had just engaged, I had that feeling. Now, using agencies and typically reviewed girls, I don't worry about it at all. These aren't the type to stop taking birth control meds or go for too long without checking their IUD. It was, frequently, an iffy feeling with some chicks, but not the last many years. And, for some unfounded reason, I trust Asians on this topic more than others and I only fuck Asians these days.

A vasectomy is minimally invasive and out-patient surgery that takes less than an hour. Just schedule it on a Friday so you have the entire weekend to recover. One of the best things I ever did for that kind of peace of mind.
Once you get to the point in your life where you know you're not having any more kids, do it. It allowed my wife to get off birth control and get rid of all those side effects.  Win - Win.
Do it when you know there's going to be an event on TV where you can sit and watch all day. Although binge watching a new show would work too.