Hi Whit!
Congrats man! I'm not a surgeon, nor medically trained, but I can tell you, from the testimonies of many "hippies" that a resurfaced hip is very stable. Most doctors, in reference to resurfacing, do not even prescribe the 90 degree rule. The only "move" to be careful about, until your hip capsule fully regenerates and the surrounding and supporting muscles/tissues/ligaments is the knee-up-towards-chest (yes to that 90 degree mark!) BUT with internal rotation - as if to cross your legs. But usually, a person after surgery for some time is too tight/stiff to even get that far anyways.
As for cycling, it, like swimming, is one of the best activities in your recovery period. It is so repetative in nature - the spinning - that its like constanly stretching and releasing ... which helps so much in regaing range-of-motion. I'd recommend switching your road/mtb pedals for flats (I know, yuk!) at first, until you have the confidence in your hip. It is very stable. If you use your road/mtb pedals, just back off the tensioning spring(s) - usually with and 2-3mm allen wrench, depending on the make of your pedal. If you are going to ride on the street, ride in a very "traffic-calm" area. You don't need a fall or a run in from an aggressive driver because you're riding a little slower
This will make you laugh - hopefully - on one of my first rides, on my road bike just after resurfacing, I got chased by a HUGE dog and had to SPRINT, with a brand new hip -well it was at 8 weeks at this point. I had to modify my position to accomodate my inability to even bend towards the 90 degress - a shorter stem, and I even moved my saddle forward a bit. keep measurements of your current position if you are going to change it up to change it back when you're all healed and ready to rock it!
Cheers man!