As others have noted, you probably mis-heard, or the person who overheard made a grammar error. We say "bumped into" -- not just "bumped" -- to mean "met by accident". So you might say, "I was at the store yesterday when I bumped into an old friend from college." Meaning, you were not planning to meet this person, the meeting was accidental.
Literally, to "bump" something is to run into it, but not in a way that is violent or destructive. Like you might say, "I was walking through the room in the dark and I bumped into a chair." If the impact is large, we'd use a different word. Like, "My car bumped into the sign post" would mean that you hit it, but there was little or no damage. "My car crashed into the sign post" means there is significant damage. So when we say you bumped into a person, it's a metaphor. You problably didn't literally collide with them. You just met them unexpectedly.
Similarly, you could say you "bumped into a problem" meaning that it came up unexpectedly. Like, "I was trying to get the Foobar Project wrapped up yesterday, when I bumped into a problem with the framnitz regulator."
To "face" is to point in a certain direction. Like, "I faced the window and looked out over the parking lot."
You can say that someone "faced a problem", meaning that he acknowledged it, he recognized that it was a problem. Like if you say, "Jack refuses to face the fact that his laziness will get him fired", you mean that he refuses to accept that this is a real issue. Conversely, "He faced his fears" means that he acknowledged that he was afraid and was prepared to deal with that fact.