The general rule is to give the new bunny two weeks to settle, without any prebonding. Then, after that do a month of prebonding.
This is because when a bunny is in a new house, they often feel stressed and so you don’t see their true behaviour. So some people (not you of course), might see new boy not being aggressive with the existing girl, and say ‘oh great, they’re bonded’ and then a month down the line, when the new bun isn’t so new anymore, he decides to try and assert dominance and suddenly they’re fighting. We see this happen quite a lot here, so really, my main advice when bonding is to take it slow, even though that can be frustrating.
The fact that he runs up to you for head pats normally makes it seem like he is feeling stressed in the bonding situation, as clearly he’s not generally a super shy/skittish bunny.
So, I would advise that you spend at least a month prebonding from now. The fact that your resident bun got really angry when he was in her territory is another big reason to pre bond – she needs to get used to the idea of him in her space so that they can live together once they’re bonded.
Can you split her space in half with some pen walls temporarily? You’ll need a double layer so they can’t nip each other through them. Then you’ll need to swap them between sides every other day, so they both get to smell each others scents all over the place, and your existing female stops seeing all the territory as hers. She probably will be extremely angry at the beginning, but that’s normal, and she’ll get over it.