Not possible. The PSP sandbox doesn't have access to any bluetooth functions, it's simply the way the sandbox was written, so it's logical to assume it doesn't have any bluetooth-related functions either. I assume it's because there would be compatibility issues with the hardware the Vita uses compared to what the PSP Go used, or something along those lines.
Custom Bubbles wouldn't do anything to help, either, since it's still launching the games in PSP mode. There was one trick over a year ago that let you launch PS1 games via Tekken 2 on the Vita, but that was obviously fixed since then, so you won't have any luck there unless you're still on the required firmware for some reason and have Tekken 2 installed.