Advice needed on travel

Hello people I'm planning to go to Kullu in Feb and we've booked a flight which reaches Chandigarh at 6am. How do we get to Kullu from there? We checked out buses online and all the direct buses to kullu are in the 12am-5am window. We couldn't really figure out cab prices so that's an option as well. Can you give me advice on what to do here? It would be very helpful if you could tell me about the cab and bus costs, and the best way we can reach Kullu from Chandigarh. Thanks in advance