To me, both are correct. I prefer the second sentence.
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Argo80 Would you like me to bring you some water?Please don't put a space before a question mark.?
To me, Would you like some water? implies that you'd like to ask someone who may need a glass of water.
In your examples, you are asking someone who may specifically want you to get him/her some water.
What's more, people usually say "to get you some water" instead of "to BRING you some water".
Let's hear more comments from other professionals. Cheers!??