We had pretty much exactly the same problem with our first two dc: dc1 was mix-fed, so dh had a lot of involvement feeding him, whereas dc2 was bf and dh felt very left out and felt he was not bonding with her at all. Fortunately hr brought this up himself when she was about 6-8w old.
TBH I felt quite angry at him - knowing the difficulties I had had feeding dc1, and how I had spiralled down into PND, how dare he feel anything other than joy for us that things were going well, and how cruel of him to want to compromise this delicate new feeding relationship by introducing unnecessary bottles?! Surely him not feeding dd was an acceptable compromise to avoid me developing PND?
But then I thought about it some more, and realised that dh was part of the reason I was OK. It wasn't just that bfing was going well this time, but also the huge efforts dh was making on my behalf. But while I knew I was OK, all dh saw was the exhaustion I felt - which looks similar to PND. There was very little positivity in our house at that time. We felt like we were constantly on exhausted tenterhooks, constantly watching out for the demon depression. Dh needed some happiness, some pure, innocent, cherishing.
I reminded myself that dc1 had managed to combine bf and ff without any nipple confusion, and that dc2 was now much older than dc1 had been when he started on ff, so it was much less likely to compromise bfing.
So I decided to unclench and let dh have the opportunity to feed dc2. As I'm not a good expresser, it would take me several sessions over several days to get enough for a good feed, which limited the bottles to once or twice a week.
It was an acceptable compromise. Did not affect our breastfeedi g relationship at all (bf/ebm until weaning, then continued bfing until 24m) and gave dh such joy and a huge boost.
I also backed right out of the bathtime. Left dh completely alone with the dc until he called me back for dc2's bedtime feed.
HTH