Light transport pilot reported ATC issued a low altitude alert during approach into BZN. Reporter stated the PIC may have programmed an incorrect approach and added that the autopilot became disconnected; but was not sure how that occurred.

Narrative

On Date I was assigned to fly with a PIC that I haven't flown with before. We were scheduled to fly from ZZZ to BZN. I have been to both of these airports a few times and I felt comfortable flying to them. As I haven't had any issues flying to BZN before. We began our descent and I received the ATIS as early as possible and advised the PIC that Runway 30 was in use. GPS and Visual. The PIC discovered that there was no approach to Runway 30. RNAV (GPS)-A was in the FMS and available. The PIC built the RNAV (RNP) Runway 30; I believe he did this in error and meant to select RNAV (GPS)-A. I noticed the PIC spent a considerable amount of 'heads down' time on the FMS. I don't think he heard ATC ask us to descend from 13;000 to 11;000; at that point I said to him that I will initiate a descent to 11;000 at 1500 fpm. The AP and AT was armed and the aircraft began a descent. I was then asked to build a 5 mile final to Runway 30 which I tried to do but a message came up as 'unknown waypoint'. I made a few more attempts to correct the situation; but did not have enough time. We were then instructed to fly to PESRE. And at that point ATC advised of a low altitude alert and climb to 11;000. I'm not sure how the autopilot became disconnected. I was not the pilot flying and I never touched the controls. I do want to mention that the PIC briefed me to not touch the heading bug. This was mentioned when we were starting engines in ZZZ. I also suggested to the PIC that since we were VMC and I could see the airport environment and I made a gesture pointing to the general location. But I guess during the workload he didn't hear me. At no time did the GPWS activate.The PIC needs to improve CRM and delegate during high workloads. I was using the checklist as assigned.