How would he know Bill was going to be there?
Thanks to the miracle of time dilation, he would have had years (or months or weeks, whatever, can't remember if they actually gave a timescale) to prepare between seeing Bill step out of the Tardis and her capture. He might not have known the exact period she was from, but could make a reasonable guess from the clothes that it was within 20 or 30 years either way of his time as PM. It seems sensible to err on the side of caution, not knowing for sure if she would recognise him. Plus, he does love a good disguise, does the Master, by 'eck.
Even if he wasn't working in the hospital already, the Master (like the Doctor) would probably have little trouble getting accepted and carving himself out a niche. It's what he does. It's what they both do, in fact. That sexy Gallifreyan charisma, etc. Oh, and a bit of mind control, though the Master appears to have a fairly poor success rate when considered over the course of his various incarnations.