Could this be begging the question?

Seems  to be a valid Modus Ponens argument. to me. The antecedent (being at the table) is affirmed. Is it actually true that Jim is at the table? If so, then the poor guy is bald.

Nope, the category X (people at the table) has property Y (they are shaven). If A is a member of X, then A has property Y by definition. The argument works.

Is it assuming the truth of premise 1? Yes, but that isn't what begging the question is. It's a question of whether P1 is a valid observation or not.

Nope, its a logically valid argument. 

All X have Y.

Thing 1 is an X. 

Therefore, thing 1 has Y.