Dear Dipali.
It is not easy to specify the origin of belly dancing in ancient times. There are different theories about it and there are quite some books presenting those different opinions. Some researches say, belly dancing has its origin in the birth rituals of Black Africa, others say, it comes from the Astarte (Ishtar) rites of Middle East, others again say, it has it's origin in the ancient Greek rituals for Aphrodite (Venus) (I like this version the most, since I am Greek
). Nevertheless, we cannot not know for sure.
As about Egypt, it is definitely the mother of the contemporary belly dance and still the most important belly dance country. It is not true, that belly dance is ignored in Egypt today. It is in a more difficult position, than it used to be 20 years ago, because of the growing Islamic fundamentalism, but Egypt is still the source for the art of belly dancing. On the other hand, it depends, what you call belly dancing. As you know (or at least, I hope you know), there have developed different styles of belly dancing in the past 40 years, but some of them are so different from the original Egyptian/Arabian style, that I'm not sure, if one can still call them "belly dance". If you want to know more about the styles, have a look at the forum "Dance Styles"
http://forum.orientaldancer.net/forumdisplay.php?f=5
Regards
Chryssanthi