Hey buddy, from jaipur you can get a train to chandigarh which is almost everyday, I guess at 4:30 pm and it will be a overnight journey so its quite good, from chandigarh you can get a direct bus to kasol from isbt sector 43. The local bus from chandigarh takes so much time to reach kasol so I will suggest you to book an online bus from chandigarh to kasol in night and roam around in the city during the day. You can also board a bus to kasol from delhi at the same fairs on redbus app. Have a nice trip.
Try staying at "River View" hotel in kasol. It has a great view and is affordable as well. Apart from that, the food in Kasol is overpriced so I would recommend you to carry bread, butter, Nutella or something like that if you want to save some money.
You will get a direct bus from Delhi to kasol at 8pm from kashmere gate and since your traveling solo, try staying in tent on Parvati valley.
and stay on the bank of the river, it'll be very nice. if time permits go to manekaran which is 3kms far from kasol if you like trekking, go to rasol which is 5 hrs duration trek.