Just tried to get a mutant bike today - Will try again tomorrow. It might be as random as the Cop Car in Reuniting the Families for PS2 players. Today's attempts are as follows:
1) Did not get to Transfender in time
2) During the proper cutscene, bought the wheels, but when I wanted to buy the paint color, it said I already had that color (really !?!?!) then tried another color but not in time
3) Got to transfender - waited 20 minutes. No Go
4) Got to transfender - waited 45 minutes. No Go. Exited. looked at radar, see 2 blue blips, 1 red. Reentered. 20 Minutes. Same result. 2 Blue, 1 Red.
I did noticed the Ghost Town effect goes away when exiting Transfender. (Meaning there is regular traffic) even while the mission is still going and Smoke can't seem to kill the last 2 guys.
Attempt Number 5 - I gave Smoke a little bit of help. I guess let's describe it as this. In addition to shooting the two guys you need to, I also shot the guy closest to where you jump over the ledge to run towards the store and get the bicycle. A BF400 with WIRES wheels on it, very nice. The wire spokes only show from the passenger side.