Can my manager ask to see the hotel bill for my vacation?

As long as you are following the company’s policy in how and when you put in for vacation pay, what you do on vacation is your own business.  You could take a vacation and sit in bed for the two weeks watching “Seinfeld” reruns.  As long as you are not doing anything during your vacation time that would cause you to run afoul of your duties to the company (e.g., moonlighting for a competitor when you’re not supposed to), and as long as you have reached the point in time when you are actually entitled to vacation pay, your manager has no right to ask.  Have a look at your employee manual to see if you have followed all the steps.  You may also want to speak to someone in Human Resources about the situation.