You don't have to rush in and have a conversation. Just start by smiling at her when she walks past. If you do this a few times and she smiles back continuously, then up the ante by saying "Hi" when she walks by. If after doing all this she seems friendly to you, then starting a conversation won't seem so awkward.
Do you share any of the same classes or other activities?
Never regret anything that has happened in your life. It cannot be changed, forgotten or undone. So, take it as a lesson learned and move on.