Can I claim a deduction if I made a charitable gift to a non-profit by purchasing a travel package that the non-profit was auctioning off at a fundraiser event?

The amount you can deduct is what you paid OVER FMV for the trip if you used the trip.  If you gave it back to the charity or didn't use it then you can deduct the entire bid price.

You don’t need to know the price the nonprofit paid. You need to know the fair market value of the travel package, what it would cost you to buy the same travel arrangements at an independent travel agent.  Your deductible donation is the amount you paid over the fair market value, if any. You would also need a letter or receipt from the charity documenting this fact.