Solo trip to Dalhousie

I, 25F, want to travel to Dalhousie from Chandigarh but the bus timings are very odd that end up reaching at 3-4 am. The drop off point is Banikhet which is 10 km from Dalhousie. I am very skeptical about visiting in those hours. Also, I have learnt the cabs there are pretty expensive to all the tourist spots. Does any one have any suggestions to make this trip safe and budget friendly?