With a fish in cycle it's a bit of a balancing act. You need the ammonia to kick-start the cycle, but too much and your stock suffer. So water changes will help your stock but may slow down the cycle a tad.
You can use Prime to detoxify the ammonia but it only binds it for about 48hrs at which time it will revert back to its toxic form, so you'd have to add more prime after this time.
It renders the ammonia harmless to your fish temporarily, but your growing colony of BB can still absorb it, which is exactly what you want.
I think this would be a good course of action for you, if you have some Prime.