The book says something like "Anarchy doesn't concern itself with movement speeds", it also lists a use of Athletics to be Running, but doesn't explain how that works. Rolling Athletics/Pilot as an opposed roll and awarding the winner by closing or increasing the gap by 1 range category might work fine if the chase begins as close range or maybe even near range, but it seems tricky when it's further than that. One other thing to consider is slow tanky vehicles vs fast squishy vehicles (van vs bike), statistically the van is much stronger, so as the GM I would give a bonus to the bike, perhaps +2 or +3 dice, that way you can't just power game and use big tanky vehicles with no drawback.
Not allowing plot points to be spent on movement during a chase scene seems like a good call as it quickly devolves into everyone doing so. To recap, how does this sound?
The faster vehicle grants the driver between +1 and +5 dice depending on vehicle speed disparity
Plot points cannot be used to increase speed during chase scenes
Opposed Piloting/Athletics to determine if gap is closed or expanded by 1 movement category each turn
If the fleeing party moves beyond far range they have escaped
When obstacles come up you have to roll Piloting/Athletics to avoid a crash
In some cases you may have an opportunity to take a risk and catch up or retreat by 2 movement intervals, this requires a difficult vehicle test, your pursuant gets a chance to match your success