Ostensibly she didn't - that scene where Ted shows up, the conversation he interrupts by ringing the door is them teasing each other about it. It's hard to know, though, because we never actually see Babs find out, and when she finally does just casually call him out, it's made clear that she's known for a long time and just let him think otherwise. Which is actually a pretty interesting statement on their friendship; not only does she seem relatively okay with him knowing more about her than she does about him (which even now vexes her like mad, but back then was almost inconceivable), but she's actually willing to let him lord it over her when she could stop him.
Anyway, regardless of whether she knows who Tim is or not, I'm sure she knows he's not Bumblebeeb. Tim would never abuse smileys that way.