Bus starts from recongpeo at 6 or 7 in the morning which Is the only direct bus to kaza. u need to reach recongpeo a day before. u can choose to either go till tabo or dhankar and stay there overnight. if u r alone .. u can also go for hitchhiking to reach spiti since its just an hour from dhankar.
Hey ! Yes , you can completely see using public transport. Depends on your budget also If you are going from Manali , the bus will cost you 300 INR. Once you have reached spiti, you can get cabs there. There are lots of solo travelers who come. You can ask them to join you and hire a car for day trips. Let me know if you are interested in detailed itinerary . I can mail it to you 😊