Assumption, then question.

So, assume Larry Craig was soliciting the undercover entrapper/policeman for sex.

Is it a certainty that he wanted to do it there, in a semi-public place, and not go back to a motel room?

No, it is not.

ASIDE: Instead of resigning, Craig should switch parties (perhaps to the Libertarians.) That would certainly teach the Republicans who are gleefully throwing him under the bus a lesson. Then, whether or not he stays in Congress would be none of their business.