It wouldn't make very much difference. Let's quantify how much.
First, estimate the volume of a bicycle tire. Most you can encircle with your thumb and forefinger, which gives a cross-sectional area of order $\pi\rm\,cm^2$. A "700c" wheel is named for its diameter, about $700\rm\,mm$, so the circumference is a couple of meters. That gives a bike tire volume of about $600\rm\,cm^3$. There seem to exist mountain bike tires with diameter five inches, so the high end of tire volumes is thirty or forty times this large, perhaps $24\,000\rm\,\rm cm^3 = 24\,liter$. Let's use this volume.
The buoyant force exerted by a fluid is equal to the weight of the displaced fluid. The mass of $24\rm\,liter$ of air is about $24\rm\,g$. This isn't very much lift compared the the mass of a typical cyclist. In fact, switching from typical rims/tires (which was saw would provide roughly $0.6\rm\,g$ of lift, if you'll forgive me providing a force with mass units) would probably increase the mass of the bicycle by more than $24\rm\,g$, so you'd come out heavier rather than lighter.
A bicycle tire should roll along the ground without slipping. (Rolling friction comes from the wheel's motion around the hub, and to a lesser extent from deformation of the tire near the ground.) If you could provide a significant amount of lift, the tires would be more likely to skid during hard starts and hard stops, but rolling friction wouldn't be very different. Providing this much lift in the tires would make the bike vertically unstable --- it'd want to flip over, with the tires in the air and the cyclist on the ground. In such an inverted configuration, you'd go slower and find the ride less comfortable.