I have crossed the canyon many times - but in involves hiking the North Kaibab and either the South Kaibab or Bright Angel as well as shuttling your bicycle on the shuttle service.
First - the North Rim doesn't open until mid-May.
Second - the shuttle service usually doesn't start until after Memorial Day.
Third - the shuttle service does not normally offer this service.
You need to know precisely what you are doing and make special arrangements.
Fourth - you must get a backcountry permit to camp in the canyon.
(These are very hard to get on short notice.)
Fifth - Or you can stay at the Phantom Ranch bunkhouse.
(This is almost impossible to get on short notice.)
If you take a bicycle on the canyon trails - not only are you crazy,
but you will be arrested, fined, and your bicycle will be impounded.
Considering that you do not seem to know the particulars of hiking/biking in the Grand Canyon -
I suggest that you enjoy biking from rim to rim via Lee's Ferry.
US 89 between Lee's Ferry and Cameron can be busy with narrow shoulders.
Caution is advised.http://www.crazyguyonabike.com/doc/page/?o=RrzKj&page_id=26347&v=QK