Can I do an internal bleaching on a tooth that has a ceramic crown?

You pose an interesting question. The short answer is yes. As the other dentist suggested the access hole weakens the crown--that said, it would be a more conservative option before replacing the crown. Certainly an option to try. Good luck 

The crown would have to have a hole drilled into it in order to access the chamber for internal bleaching. You risk the crown fracturing or coming off. Then the hole would be patched with filling material. That can sometimes leave an area that isn't smooth or can trap food and cause decay. You should discuss the risks/benefits with your dentist prior to making your decision.