Talk about it with her, but do expect the worst if you do. You can breakup before you attempt or leave a note. But to me it's best to talk about it, presenting it as passive suicide idealation first is for the best. Usually nobody tries to send you to the ward for passive suicide idealation. And it's easier to accept than something like "I want to die, and you can't save me."
If they react badly to you opening up because it's too much of a burden or whatever, I'd say she's not a good option to be in a relationship with since she's unwilling to support you even once.
I'm not sure what exactly causes you to be on this site so I don't know if it can be worked out and if you want to.
Also I don't have a lot to work on so I'm just assuming she doesn't know of ur mental problems at all.