"Puedo tomar/coger (un poco de) pan/agua?" Verb "tener" here doesn't suit, because it always refers to possession in Spanish, while in this case we are talking more about obtaining/use/need of something we don't have. The quantifier "un poco de" can be omitted, but when used it means that the quantity of the item involved ("agua, pan") is limited.

It depends a little on context. If you're asking for some at, say, a cafe or restaurant, maybe something like, "me gustaría un poco de pan y agua." Less formally you can say, "¿me puedes dar un poco de pan?" Although strictly speaking you don't need to say un poco de, since just "me puedes dar pan o me puedes dar agua" could suffice.