An addition to my question: I don’t do business directly with him. However, he appears to be an executive. He gave me his private contact information specifically to me, so I don’t think it was just a courtesy.

If he gave you his private contact information, it doesn’t sound like this was work-related. I think you should consult your supervisor. It’s surprising that, in this day and age, someone in such a senior position would blur the lines between their personal and professional lives so much.

If this isn’t an invitation to dinner for work but rather someone looking for a casual sex partner, they won’t offer you an allowance. If they’re not your type and you don’t think they’ll offer an allowance, I’d suggest consulting your supervisor and asking them to help you come up with a way to decline. Since this involves work, it could hurt the company if you turn them down inappropriately. Please try not to react emotionally, and consult your supervisor.

You’re the only one who thinks you’re the only one—he may be approaching other women, too. So I wouldn’t get too excited thinking, “He specifically chose me!” If you feel like, “It’s just dinner, so why not?” then go ahead. As I mentioned earlier, if he’s married and you have absolutely no interest in that kind of relationship, but you feel you should go because he’s a business partner, then bring a coworker or supervisor along to dinner. If you don’t want him to dislike you, want to make a good impression, and think, “I’m special to him!” then just contact him and go out for dinner. The fact that you’re asking about this on an anonymous papa-katsu Q&A site probably means you’re at least wondering whether there might be an allowance involved, doesn’t it?!