Hey, so I am actively going through this at the moment sort of. My male cat James was aloof to the new female Jessie, but Jessie loves to run up to him hiss and swat. I immediately noticed a behavior difference in James, from cute and cuddly to skittish. She was basically hunting him down and attacking, hissing and swatting and causing him to run.
First thing that helped was a baby gate door between them then a feather toy in that gate and treats on either side. Get them close without feeling threatened that was big. You need to use 3 baby gates in a doorway to block the entire thing off.
Then I let them in the same room with 100% supervision. Both were bonded to me and I was confident neither would hurt me so I basically crouched over James as he did stuff and if she came over to hiss id push her back. Honestly this kinda worked as she wanted to be close to me but realized quickly I wasnt going to let her hurt james. I did get a few scratches breaking up a fight, (I am covered in Tats so I dont fear the little ones but I don't recommend you doing this).
I basically acted like a barrier to the one being bullied in the room, now they can both sleep on my legs touching and not fight. It isn't perfect yet, if he touches her she gets mad (although she cleans him). But muffins mood has come back to being a love suck and cuddly.
They are now able to shared a litter box and food and water and I dont fear them being along in the house together.
She does still hiss a bit if im playing with her and he comes over and tries to play with the toy too. But with some quick maneuvering I can get them to share and take turns.
Cats are territorial and at some point they will need to work out a hierarchy.
It took over a week for them to get along. The first few days I thought there was no way they'd ever get along, and when I saw his mood change I almost considered bringing her back. Was very stressful. Thankfully it got better over time, and continues to get better. I now see James push her around sometimes, and she pushes him around sometimes haha.
** Disclaimer **
I do wish I would have taken the advice on the forum more seriously, a slower introduction would of saved them both a lot of pain im sure. The advice I got from the breeder was to leave her in the cage for an hour in the room then let her out and let them solve their issues and they'd be playing in a few hours. THIS DID NOT WORK, she bullied him overnight and I was forced to start again from a worse off position.