If this means keeping the Ugly Friend engaged in conversation, then so be it.__B)..you both like the same person.__Then neither of you should actively go after him or her! If the object of your mutual desire approaches one of you, but not the other, the lucky one should really think twice before flirting back.
What if you hate your BFF's current significant other?
When you're out together and single...__A)..one of you likes someone.
__Then the other really should help initiate conversation with that person, and once the ice is broken, extricate herself from the situation.
Whether it's someone you're meeting online or it's someone your friends know, aim to drop the things you know about them and start fresh.
Don't ask your friends to tell you everything they can because you can end up with a tainted view of what to expect.