Yes, you can bicycle from your hotel to the Sugar Loaf cable car ticket office in Rio. In fact, the biking lane goes from Leblon, Ipanema and Copacabana (the nicest neighborhoods and where most tourists stay) all the way to Urca neighborhood, ending just a few steps away from the cable car ticket office. From Copacabana, for example, cycling would take approximately 20 minutes.
Notice that you would need to rent a locker to store the bike nearby the ticket office, since you would be away from your bike for approximately one hour and a half while visiting Urca Hill and Sugar Loaf. Most bike shops in Rio though rent bike lockers along with the bike (usually for a small extra charge).
Beware that there is no bike parking lot next to Sugar Loaf box office and you can not bring your bike into the cable car either. You would need to look around for a fence or something else where you can lock your bike. The area next to Sugar Loaf cable car ticket office is very urban, so you shouldn’t find problem in locking your bike.
Although the area around Sugar Loaf is very safe and patrolled by the police, locking your bicycle is a must.
See here photos of both: Sugar Loaf and Christ the Redeemer statue atop Corcovado Mountain.