I could be in error on this, but Bee is on track to becoming AZ State Senate President for the 2007-09 session and may wish to use it as a jumping-off point to run for Governor in 2010 when the seat comes open. He just may not be interested in federal office and being a backbencher in DC when he's a power player in Arizona.
Tim Bee seriously explored running for the AZ-08 open seat and is term limited out of his current office in 2008. The best explanation in my view for why he did not run is because he considered it too risky compared to the alternative (an excellent shot at AZ Senate President).