Well they don't expect you to bow to them as it is not your culture. You can just not do it and get away with it because they aren't expecting it. You could do something that is called eshaku which is like a head nod. You don't bend your body over.

Please understand that it's a part of the polite greeting, however, between close people, there are cases that we don't bow. It's not an obligation if you travel in Japan, but if you work here in Japan, it's needed when you greet with your bosses, clients and your co-workers who are older than you. It's our culture like that it's forbidden in the Islamic faith. We have our own culture and way to greet, don't we? I think we have to respect each culture and if you have some that you don't like, it's OK, you have option that you don't choose them and no one can criticize you. It's my opinion. I hope you understand it.

In the Islamic faith it is forbidden to bow to people/things

Just out of curiosity, why would you want to avoid that?