Feeding your bp in a seperate container is a topic that has mix opinion's. When I first started keeping snakes I alway's thought that your suppose to put them in a different container? It's not a bad thing to do (but, for me I don't do it anymore.). I also keep larger constrictor's and so it would be very time consuming and possibly dangerous for me to handle a large constrictor when in feeding mode.
I don't have any problem with feeding in the tub or handling my snakes in the same tub on non feeding day's. I have been striked at once at the beggining but never since.
One benefit in taking your bp out to a feeding tub , is that you won't have to worry about substrate getting caught in the mouth. You'll just have to do what you feel is comfortable to you.
As, far as handling your snake? You never want to come down at his/her head. Before, I try to pickup my normal's,retic or anacondas. I alway's gently touch a side of them mid point of there body give or take. Just to let them know I'm there. For, my retic and anacondas I use a snake hook to do that action. At this point thou I feel confident that I don't even need to use a hook. But, I want to make sure that they associate the hook as a non threating object, especially when they get much larger. They also say to rub the head with the hook but I don't like doing that. Rubbing on the head is suppose to snap them out of feeding mode. With a bp I don't think you'll need a snake hook.
You usually want to support a snake a few inches back from the head and a few inches before the tail.