How the bus system works for you will largely depend on where you live and where you're going.
First off, if you're an undergrad, don't bother with a car--it's a royal pain to keep on campus and 98% of what you need will be immediately to hand.
If you'll be living near CU or downtown, and/or if you plan to be working near CU or downtown, being carfree is very doable. For a town of its size, the Ithaca bus system is excellent. The buses are very reliable, clean, and well-used. Most stops do not have bus shelters, but those that do are clean and in decent shape, though occasionally a map or time schedule gets ripped or falls down and is not replaced for a long time, so knowing routes is important. I don't drive (though I have access to a car via my SO) and I rarely hurt for it. I know several other carfree people who live in town. Cycling in town is a bit funny--the culture of the town is very bike-friendly, the geography much less so.
The buses have space for two bikes in the front, and if your plan is to ride downtown and bus back up, you may not get a space on the bike rack because lots of other people have the same idea.
However, if you plan to live and work near IC, or more than a few blocks from the downtown area, the bus schedule can be tricky, particularly if you want bus access at a time that is not between 9 and 6 M-F. Because the town is relatively small, the walkable urban-like area is also quite small, so some places that look close to town are very rural, without sidewalks, etc. It really depends.