Why am I thinking of that old Tony Danza sit com? "Hose the Boss" or something like that.
I say if you want the job, pass on the woman, but if you want the woman, pass on the job. But that's me, not you. However, like you, I do see how it could be somewhat innocent on her part. If she is interested, knows you may have to leave because you need work and she has work, offering you the work is somehwat logical even though it can be construed as paying for the whole package. Interest in a relationship is a binary thing - "friendship to start with" is interest. Just my opinion and possibly worth less than what you paid.