You may have to wait your turn, or your meeting may take precedence. Don't attach any significance to this situation. If you expect to launch immediately into your reason for sitting in the room, you will end up frustrated. Also expect frequent interruptions. If your meeting is with a woman, don't offer your hand to her unless she extends hers to you.
Many Indian women tend to follow the custom that governs their religion.
A Muslim woman may just nod and say hello. But don't think that these forms of reserve translate into limited business authority. Many women in India have considerable power in the private and government sectors. When you discuss yourself and your business needs, speak with a comfortable yet quiet authority. American men are often considered aggressive, so don't come on strong.