Jimmy McGill! Hi hello, one of your bodyguards reporting in for duty! The Doctor here will be an absolute disaster of a bodyguard probably, but look, he's gonna try very sincerely. Not for lack of wanting to protect him, trust me! He's a Time Lord/alien so I'm sure they can have rousing conversation; his body can sustain some damage way better than a human body so he's got you covered, Jimmy, he'll take all the blows. Just...good luck keeping him from getting distracted! He's constantly sticking his nose everywhere it doesn't belong (literally and figuratively, this guy is an alien weirdo and feel free to tell him often).

He would try to insist that Jimmy stay put somewhere for his safety and his own good, but they'd actually probably be a good team up because the Doctor is all about being clever/scheming/manipulating for the greater good and trying to help everyone. They can investigate and whatnot maybe? At least if they're stuck together, he'll be better able to keep an eye on him so it all works out.

Also please do throw a bodyguard party with some cake (or stale crackers, whatever they've got)! He'd probably try to insist on being the public-facing bodyguard because he's a social butterfly, but he can also do weird shadow lurking, too.

/phew that was a lot, thanks for coming to my TED Talk!