There is no cold water running out of bath tap but there is in all other taps

I will make the following assumptions:

1) This is a tub only, not a tub/shower
2) There is hot water

Most modern faucets use devices called cartridges. These devices go bad after a time, and need to be replaced. If your tub has separate handles for hot and cold, then you need to replace the cold cartridge. If you have a single handle, then you need to replace that cartridge.

This is the most likely problem. It is also possible that debris has clogged the cartridge or that (if you have them) an integral stop has gone bad. This last is a part of the valve itself, but can be replaced by a plumber.

I hope this helps!

Please, be more specific... too vague to offer advice... Back to you... Milo