There’s no obligation or requirement for you to finish inside her mouth during a BJ. It’s easy enough for her to either move it out of her mouth at the right time (assuming you let her know when you’re cumming) and stroke you during your orgasm, or for her to just angle it away (towards you) and lick your frenulum while you cum - unlikely to end up with it in her mouth then.
If she just doesn’t want to swallow then if she’s kneeling above you with you laid on your back she can just let it fall from her mouth back onto your cock - it makes for good lube!
For any man who’s wondered why some women have an aversion to swallowing there’s a simple test. If she’s happy for you to cum in her mouth once, get her to immediately kiss you and transfer the contents. You’ll then know exactly what she’s experiencing and it’ll give you a completely different perspective.
Some flavoured lubes taste nice, some don’t so there’s another option if it’s a purely ‘taste’ issue.
The options are endless. But no point in pushing her to do anything she’s not happy with as that will just result in an unwillingness to give you a BJ.
Good luck!