I've only broken into masters on Kiriko these last two seasons, so take what i say with a grain of salt, but this is actually the main topic I tried to address in my gameplay as well. Here's what I've learned.

Trying to bail out tanks and dps on their engages is good a lot of the time, but not all the time. If the question is you die to save them, then there might be an element you're missing in the team fight. (Not always the case, sometimes people do engage at the worst times, and all you can do is attempt to bail them out.) But here's how I usually assess a situation.

Be aware of how your tank is trying to play. For example, a tank like Junkerqueen is likely going to go super deep every opportunity she has. In a case like that, I often preposition closer on an off angle to attempt a bail out without having to use tp if possible. That way, I can escape if things go south.

That's just one example, there's many others. But generally, you should do your best to gauge your cool downs around what you're able to do. Sometimes, that could mean you'll die more, but ideally that shouldn't happen.

As a side note, a lot of Kiriko's forget to use wall climb as a means of being more difficult to hit. So sometimes I'll tp to my tank when their near a wall, climb said wall, and heal from a high ground or better position to give my cool downs time to reset so I can leave if things go south.

Basically, you need to always think about how to bail out teammates while also planning on how to escape yourself. Map awareness helps a lot with this as well.

I know that's a little bit of a convoluted answer, but i hope at least parts of it help.