Plan in early feb as after mid feb there will be offseason in Rann of Kutch..
You can opt to stay in near by resorts which will be cheaper than staying in rannutsav tents...
There is a village on way to white rann. i.e. Hodka, here you can find good resorts for lesser tarrif.. You can try some of these.
1. Kutir Craft Village Resort
2. Hodka Rann Stay
3. Rann Visamo
4. Kutch Classic Rider Camp (for solo traveler a good option)
5. Rann Bhumi You can opt to stay, and if don;t have your own vehicle, before that do hire bike or self drive car from bhuj and proceed further. You will enjoy this trip for sure.
Don't forget to visit following attractions apart from White Rann.
1. Kalo Dungar
2. Lakhpat Fort
3. Narayan Sarovar
4. Pingleshwar Beach
5. Mandvi Beach
For travelling from bhuj you can either hire self drive vehicles or you can also get AC buses to reach dhordo.. Go Enjoy this is the best time to visit... Keep on murmuring "Kutch nahi dekha to kya Dekha"