From my personal experience and from talking to other people who have watched the show, Bojack Horseman is not necessarily triggering. That said, I suffer from bipolar depression and anxiety (with some suicidal thoughts at times) and the people I've talked to who have seen the show only suffer from anxiety (to my knowledge). It's a heavy show, don't get me wrong. You might need to take breaks between certain episodes but the show handles everything with grace. It will show you the ugly side of people, but it will also show you the consequences of those characters' actions. That's the most important thing. By the end it will leave you feeling optimistic. Not necessarily good, but it will make you feel like things could change for the better if you let them.

TL;DR: Yes, watch the show. Take breaks when needed. The show is actually therapeutic despite the heaviness of it. Any time it shows something heavy like suicide, it also shows the flip side of it - the consequences and how those irreversible actions affects others.