Air carrier on vectors for visual approach to ELP experienced TCAS RA with VFR traffic that was maintaining visual separation; ATC alleged possible communications problems with the reporter's aircraft.

Narrative

On descent into ELP; we got a late hand off from ZAB Center to ELP Approach; approximately 20 miles NW of the field. ELP Approach immediately gave us a vector to 070 and a descent to 10;000 FT (from 13;000 FT). ATC called VMC traffic. We did not see it and called 'looking for traffic.' ATC gave us further vectors to a base leg for Runway 22 and a descent to 9000 FT. The VMC aircraft; a Bonanza; called us 'in sight' and was instructed by ATC to maintain visual separation. We still did not have the Bonanza in sight. ATC cleared us for the visual to Runway 22; but to maintain 9000 FT until we had visual contact with the Bonanza. We maintained 9000 FT; still looking for the traffic; when we got the TCAS RA; disconnected the autopilot; and climbed as instructed by the TCAS to about 11;000 FT. After the TCAS RA was resolved; we continued for the visual to Runway 22 and landed safely. Just after getting the TCAS RA; the Bonanza Pilot and the Approach Controller both mentioned that we were NORDO and had missed at least 5 radio calls. At no time were we NORDO. We were in continuous contact with ALB Center; but got the late hand off to ELP Approach. All appropriate procedures were followed by the crew. We're not sure why we got the TCAS RA. Either the Bonanza did not maintain proper visual separation or the Controller gave us vectors to get too close to the VMC aircraft. Better ATC coordination and hand offs from one agency to another would have helped in this situation.