Which is correct?

Bob and I - This is the subject of "will meet," so you need the subject pronoun "I."

Bob and I will meet you today.

If it were just you going, how would the sentence go? I will meet you today or Me will meet you today?
It doesn't change if Bob decides to come as well.

I will meet you

Can be sang or can be sung?

No it does not change. The way I was taught was if you removed the other people in the sentence for a list, does it make sense. In this case, Me will meet you does not make sense, however the sentence "you will meet Bob and me at the store" is correct in this case. "You will meet me" makes sense while "you will meet I" does not.

Can be sung would be correct.

This is useful. Thanks.

"Bob and I will meet you today" is grammatically correct since "I" is a subject pronoun—not an object pronoun. "me" is an object pronoun, and should NEVER—yes, I mean it—EVER should be used in the subject of the sentence.

We can also mention it as below
'I will meet you'
'Bob and I will meet you at the store'

Your answer, though a good one that I agree with, reminds me of the joke my 5th grade teacher put on the board forty years ago. " 'Me' can never be the subject of the sentence," just proves the exception to the rule. In that sentence, which word is the subject...?