It's quite weird he wants to stay in the room, it's odd your friend doesn't suggest him going out or you two going out.
To me it smacks of controlling behavior. Especially if he takes over the conversation.
Why not invite your friend out somewhere.
If he tags along it is a real red flag to me and I would ask her if he is stopping you seeing her alone.
I'm very surprised anyone wants to get to know their friend's boyfriend. Maybe if this really is a long term relationship then you might get to know.
onlyk "Also he seems to be trying to make an effort with you" No he doesn't he is taking over the conversation and making it about him.
"...but by trying to exclude him from the conversation you could be coming across as rude and putting your friend in an awkward position." It'snot rude for women (or men) to want to see their long term friend's without friend's partner.
IMHO it will only be making it awkward for friend if the boyfriend is a controlling bastard who wants to control his girlfriend's social life. I'd say that is a possibility, but also it is possible he doesn't understand friends sometimes want to chat without their 'other half' around.
Why not talk to your friend and ask her how she feels about not meeting you one to one.