When I was little, I thought Bert was Ernie's uncle for a while. Bert was old enough to have a job of some kind and pay the rent while looking after Ernie. When we try to think about how old they are, Bert is obviously the more mature one while Ernie is the kid. I don't see them as gay, but more of a kid/adult dynamic.
I thought about the Bunsen and Beaker thing too. Aside from another Laurel and Hardy type of pairing, Beaker puts up with all the Muppet labs craziness because he helps put all these inventions together (he's the assistant, right?) so, he must have some faith that at least some of these ideas will work. Steve Whitmire said in an interview that Beaker is really smart because he works in a lab (makes sense), but he just gets the short end of the stick all the time. Fat Blue (or Mr. Johnson, if you prefer) is the same way. So is Charlie Brown. All three of them look forward to something great (kicking the football, eating a good meal or showing off a new invention), but it never works out. It's not their fault. They all try, but luck just isn't on their sides.
Another reason Beaker sticks around is a theory I had that came from one of my old Muppet books. (I'll have to look up which one, but I think it was "Case of the Giant Chicken"). It said that Bunsen was the only one who could understand what Beaker was saying. Don't know if that's true or not if we asked say, Dave Goelz, but it might explain why beaker can't get a job anywhere else.
Bunsen, I think, is so focused on the experiment and so confident (and proud) of what he built, he's ignoring the obvious, which is that his inventions hardly ever work right.
Or he could be a really quiet, calm version of the Robot Chicken mad scientist...