Mailing perfume domestically.

Everyone else has basically covered it very well. In the US = fine to ship, no worries. Overseas, be creative with your customs form so that it doesn't trigger the perfume=alcohol=flammable button.

I'm only typing this repetitive comment to give the obligatory dissenting opinion on the matter of tape. Tape makes people feel better. However, if you have a real leak, the tape most people buy ends up being very messy. When saturated with oil, the cheap white plumber's tape will actually start to dissolve and becomes a horrible sort of half dissolved oily, plastic, mess. It works OK, with traditional perfume samples, but something about the oils can really do a number on it.

I don't have a picture of a leaky imp with tape, but this picture of a leaky bath oil bottle that had been covered in Saran-Wrap illustrates the kind of mess I have seen:

http://i14.photobucket.com/albums/a320/kakiphony/Icons/IMG_0009_zpsooqhkelk.jpg

(I have used Saran-Wrap outside the bubble wrap before. However, directly over the perfume container it will do the above in a leak scenario. GROSS.)

I simply wrap the perfume container in bubble wrap and then put it in a ziplock bag. This prevents any leaks from spilling in the package, but produces no crazy weird chemical mess if there is a spill.

If you DO feel obligated to tape, I would try Blue Monster PTFE tape rather than cheap plumber's tape. It's thicker and made of slightly different material that is made to seal leaks around pipes carrying acids, kerosene, etc. I think it might be more up to the task of preventing perfume oil leaks since it's designed for more than water. However, I have not tried it.