Yes you can travel solo to Hampi. you will get autos or car on rent which takes Rs800-1200 per day to take you to nearby places a day. You have to reach hospet railway station where you get lots of stays, restaurants and transport options.
To know more, please visit my profile where I have made a 2days itinerary and will be happy to help you if you want any more infos. Do let me know about how you enjoyed in Hampi.
Yes travelling from Mumbai by bus you will get down at hospet. You can either stay in hospet which is 20-25 minutes from hampi or else you can stay in hampi. In hampi you will have to stay on hippy island wherein you can book rooms ranging from 700 and more, enough of guest houses are also available. You can try shanthi guest house which is in hippy island. We stayed in malligi resort which is located at hospet 25 minutes away from hampi but we did booked an auto for an entire day which cost us 1000 rs and he showed us around hampi (all major sites covered). For transport autos are convinent however if you are staying in hippy island you can also rent a moped.