A Corporate Pilot approaching ASE was not positioned by TRACON for a stabilized approach. After abandoning the approach; the crew experienced a near miss near 16;000 FT. Because of heavy traffic and weather the crew diverted to a nearby airport.

Narrative

Flight to ASE. I assumed the responsibilities as the non-flying pilot. Arriving at ASE the weather was IFR with the LOC/DME-E Approach in use. Contacting Aspen Approach; the Controller seemed overwhelmed with the amount of aircraft being controlled. We soon received vectors for the approach and were told to maintain 14;000 FT. We soon received a clearance to proceed direct to JARGU and to cross JARGU at 13;400 FT cleared for the approach. Our aircraft was positioned abeam JARGU when we were issued this approach clearance. Due to the performance of the aircraft both the flying pilot and I agreed the aircraft was not in a position for a stabilized approach. We informed ATC that we were unable to accept the approach clearance. ATC gave us a radar vector and were told to climb and maintain 16;000 FT. I set 16;000 FT in the altitude preselector and the pilot flying initiated the climb using vertical speed to 16;000 FT. At an altitude of 15;400 FT ATC informed us to maintain 15;000 FT. I selected 15;000 FT in the altitude preselect at which point our aircraft received a RA and the pilot flying initiated a descent. We heard on the radio another aircraft declaring an RA climb which blocked our transmissions. Our aircraft leveled at 15;000 FT only dropping below slight for the RA maneuver. Once cleared of the conflict we diverted to a nearby airport. On the ground; I called Aspen Approach and spoke with the Supervisor and told him what had occurred and asked if a statement was needed. He stated nothing had been recorded and no statement was required by the crew.