What is the max bombs and potions you can carry?

You can carry all the potions and bombs you want, but you can only carry a certain amount of the same potion. For example, you can only carry 3 swallow potions (4 when you upgrade them to enhanced swallow and so on). But things like this can be modded. There is already a mod which modifies the duration of potions, their power, and the amount of potions you can carry.

Thanks - I just thought it weird that I could have 3 potions but only 2 of each type bomb

They work exactly as potions in that aspect. Find the enhanced formulas and expand the the limit, or download a mod :)

There's also a decoction that increases the amount of potion uses by 1. So you just drink that at the start of a day (ie. after meditating) and then you have +1 uses on every potion..