Rajasthan is a popular tourist place so you will get hostels easily.. And Mumbai is well-connected by trains A lot depends on when you are travelling too
Hi Sankalp, It is usually very expensive to travel solo in Rajasthan. You can rather opt for a package, I have attached with this comment a package for Rajasthan, you can click on them to find more details about them. If you want to talk to someone about the packages simply fill in your details in the form and you will receive a call.