Ok, where were we?
What helps, what doesn't, do's, don'ts and sundry miscellanea.

Re: Feeling nothing. Yes, that's a thing. Sometimes it's anhedonia. I had a bad spell of it one time where I tried to figure out how to describe it. Here it is... That something I'd normally feel very strongly towards had all the emotional impact of a paper towel.
I've found that feeling nothing can also be from overload. It's pretty common with BP to become more easily overwhelmed than the average bear. For me anyway, this can result in just going blank. Like my brain has shorted out. You can't fix a short out. It'll pass.

Re: triggering the worst in each other. Ooooooh, yes. This can be a thing. A minefield thing. It's not like things are going to sync up. They won't. If I had to name the #1 difficulty in having a BP and BPD relationship, this would be it. Stress can be a big factor in setting off or exacerbating BP mood episodes. Chaos is stressful. BPD is chaotic. This is why it's important for each to do their best in managing their condition. So, for example, the person with BPD would be diligent in working with their DBT, therapist, etc. The BP person would be diligent in taking their meds (or alternative approach, but for most we'd be talking meds), getting good regular sleep etc. Everyone would benefit from healthy eating, exercise etc.
I won't lie. It is a HARD combo.

In terms if overall do's and don'ts... There have been threads on this where people say what they consider helpful and unhelpful. There's not as much consensus as you might think. For example, what one person finds caring, another may find overbearing. Whatever you do, avoid infantilizing. We don't like someone saying, "are you taking your meds?" whenever we get justifiably upset about something (or happy!). We are entitled to have emotions like everybody else. The corollary of this is that every little thing we do is NOT attributable to BP! We've all got different personalities, strengths, weaknesses. We're not one size fits all. We're regular people. We've just got some stuff that can cause problems for us.

When you say "asking him", has not been terribly helpful, that's not totally shocking. Sometimes it's hard to articulate what we need. Sometimes we just don't know(!) (This is true of non-BPs too, of course.) Especially for anyone not accustomed to having a support network. Some people are comfortable accepting help from others. Others are not. Respect where he's at with that. People with BP have a range of insight (awareness and understanding of what's going on with themselves). Sometimes others need to step in if it's gone wonky, but no one's going to like someone being overzealous in that (see infantilizing).

Main thing: Respect where he's at with these things. Respect and patience. I think we can all get behind those.

Hope that was helpful.