The cold water on the bathtub is not working. There are 2 separate handles. The hot water comes out fine, but the cold water will only barely trickle out.

Most likely blockage in cold water side of tub valve. Any plumbing work been done lately (pipe soldering)?
Turn off water. Remove handle and any trim covering cold water stem. Remove cold water stem. With stem removed, turn on water briefly to flush valve. Inspect washer if compression type stem or cartridge if cartridge type.

Reinstall stem.
If compression type valve you would be well advised to replace washers and seats, (hot and cold) at this time.