Your best option would be "to pull the bike out…"
As so often in English, there is nothing specifically wrong with "pull out the bike" but it is clearly unidiomatic, largely because it is awkward.
Terms like "dislodge" or "extricate" complicate the issue without addressing the original dilemma and "retrieve" carries extra and irrelevant connotations.
Let's be sure, neither the initial "Today I was trying to overtake a car and it hit me from the side, I fell on the ground and the car went over my bicycle…" nor the closing "… because it got stuck" add anything useful.
When you say "Pull/move out" has a completely different meaning, what different meaning is that, please?