If a ship is ionized and is forced to perform the ion maneuver. What happens if the ship bumps another ship before completing the maneuver. Are the ion tokens removed or is the ship still ionized.

Nothing in step 2 indicates that step 4 gets skipped if the ion maneuver is not completed. So the tokens get removed.

Page 11 of the Rules Reference describes what happens to an ionized ship during the Activation phase:

Quote

1. The ship skips its Reveal Dial step.
2. During the Execute Maneuver step, the ionized ship executes the ion maneUveR. The ion maneuver is a blue [1 straight] maneuver. The bearing, difficulty, and speed of this maneuver cannot be changed unless an ability explicitly affects the ion maneuver.
3. During the Perform Action step, the ship can perform only the [focus] action.
4. After the ship finishes this activation, it removes all of its ion tokens.

The only condition for removing the ion tokens is in Step 4 and that is the ship finishes this activation. Bumping doesn't cause you to fail finishing your activation so you remove all of its ion tokens.

Edit: What GermanBlackbbot said.

Ion rules say nothing about partial maneuvers, so it has no effect.
You still skip the perform action step like normal though since thats a blanket maneuver rule.