I think I might have some insight into the root of this problem, though it's possible that I'm misreading the situation. I have to talk a bit to show where I'm coming from, we'll see if it helps!
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When my dad bathed me I think he did a lot of the things you're talking about here.  I hated baths anyway, because I've always had major trouble with too-hot water and my idea of too hot is everyone else's idea of just right for a baby. It took my parents a while to figure out that the reason their infant was crying every bathtime was because she perceived the water to be burning hot. But they did, and I don't think I freaked out when my mom bathed me after that, even though I didn't like it.
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One time when my dad was bathing me, I remember sitting in the tub and knowing I was about to get water in my eyes. I remember the incident because I was about 3 or 4 and because it made a big impression on me. I started crying before my dad even poured the water on my head, because I knew it would go in my eyes. I think he was trying to get me to tilt my head back, but then when it poured in my eyes it would be stuck in my eye sockets, so I wouldn't. He got really frustrated that I was crying even before anything happened, and he stormed out of the bathroom and freaked out and got my mom to finish bathing me. I was immediately soothed, because she didn't get water in my eyes when she bathed me (I don't know what her method was). Knowing my dad (especially at that time), it's very likely that had she tried to give him advice about how to keep me from crying in the tub, he would have accused her of being controlling and gotten mad at her, and furthermore not taken her advice.
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I think he very much had the perspective that he was powerless to do anything to fix it, and so he just did what he thought was necessary even though it made me cry, which he hated. He's always been really bad at taking advice and really hard on himself if he can't do something "right". His solution to this (one I, unfortunately, learned from him) was to never admit there was a problem with anything he was doing. In my manifestation, this includes arguing about why I can't do things a different way (like your DH saying he can't use bubble bath).
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I'm not sure that your husband has this same thing going on in his mind, but it sure sounds like it to me. I might be wrong, I definitely tend to assume everyone is like me!
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I can't give advice about the practical details of bathing a kid, because I don't have one yet, but I think that's not the issue anyway (again, just my opinion). Does it bother your husband how your daughter reacts to baths? If he thinks that she's happy and just making a show or whatever, I don't think you can expect him to change. On the other hand, if it bothers him that she cries during baths, then you have a way to approach this that might help. It's not about what YOU think he should do, in fact, it's not about you at all. It's about her, clearly, but approach him with it being about HIM. You know he likes giving baths to your daughter and you think that that's a wonderful bonding time for them. He seems to do a very thorough job (or whatever, find a way to tell him he's doing something well). It seems like maybe it bothers him a little that she cries sometimes during baths. Maybe the two of you could brainstorm some ideas about how to keep her happier during baths so she doesn't cry? Or, if you feel like he's going to take that badly, bathe her sometimes, and ask him (as the "experienced" bather) to help you come up with ideas to keep her happy/not crying in the tub.
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It really sounds like he's defensive about this to me, and I know a lot about being defensive.Â
 I'm not sure my ideas will work, and I know it probably seems like an awful lot of effort, when he's clearly being unreasonable (just ask my long-suffering husband . . . actually he would never say it to anyone else, but I still know it's true). However, if you want this to change, you need to change your approach, whether that's reasonable or not. If he's feeling attacked, he will do whatever it takes to defend himself - like deny that there's a problem, deny that there's anything to be done about the problem, deny that the problem has anything to do with him, etc. I know it seems ridiculous to a) think everything is an attack and b) deny it instead of trying to fix it, but it's really really hard to break that mindset if you're in it. So I recommend trying to make it really clear from the outset one of the following: 1) there isn't a problem, everything is okay, but it could be just a tiny bit better, 2) he isn't the problem - he's the solution.
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Incidentally, my husband has much poorer fine motor control than I do . . . I don't know if that's common, or if it's the case for your DH, but it might be worth considering that he has a really hard time being as gentle as you, or doing multiple things like holding a washcloth to her face while rinsing her hair.
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Sorry, that was a super-long response, which is something I always tend to do. If it's relevant, then maybe it can help you (maybe even in other aspects of your interactions with your husband). If it's not relevant, sorry I wasted your time!