Wirelessly connect a BEFW11s4 with a WRT54G router to create a bridge

"DTM" hath wroth:

No. You need either a wireless bridge feature or a WDS feature in both units. The WRT54G has this with alternative firmware (i.e. DD-WRT, Sveasoft, OpenWRT, etc). The BEFW11s4 has neither. It is also considered good form to have both ends of a wireless bridge use the same hardware to avoid compatibility complications. I suggest buying another WRT54G and installing alternative firmware.

I'm told the WRT54G v5 will not accept aftermarket software.

Correct. The WRT54G v5 and WRT54GS v5 use VXworks and not Linux. They cannot handle alternative Linux based firmware.