Welcome to BB! I am not personally experienced with bonding, but I’ll share the information I’ve learned from people’s experiences on the forums.
First, an unfixed rabbit can stir hormonal behaviors in a fixed rabbit, so although Burkey is neutered, her being unspayed can make him act on hormones (as you saw).
If she’s continuing to run away, you should stop trying interactions immediately so she forgets Burkey. The first experience was clearly very traumatic, especially for a young rabbit (thumping in fear). And if you’re seeing Burkeys charging, that’s also very bad. The more bad air between them, the more difficult it will be to try and bond them once she’s spayed + a month after she’s spayed.
In terms of free roam, you do want to try and give her time outside her cage, so putting Burkey in an xpen temporarily when she has time out may need to be your solution until it’s time to introduce them following the month after her spay (ample recovery time and time for hormones to dissipate post op).
She’s very young and it’s a new environment. Focus on getting her feeling comfortable in your home and with you. Right now, she may just perceive this new place as a territory for a very aggressive male rabbit, rather than a loving home.
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.