Let's assume for a moment that home attendance is roughly correlated with fan support, and subsequently, bowl attendance. I've pasted the requisite NCAA data (from 2007, which is the newest available year at the moment) below, sorted and ranked by conference.
No doubt, there are a lot of qualifiers to this data. For instance, Rutgers and Louisville are both in the process of expanding in response to increased demand, and others likely are too. Certain schools have a rep of travelling well or poorly, which does not perfectly track home attendance figures.
Still, these figures are quite sobering. There are two ways to go about improving the BE's bowl bids at this point. If Charlotte is to remain as the #3 bowl tie-in (hopefully, with a higher payout), then the Big East needs to find a game for its fourth-place team that is more appealing than Birmingham and Legion Field. If the Big East is looking to find an equivalent to its old Insight Bowl tie-in, then it has to find a situation where its #3 team (ideally, Meineke would then drop back down to #4) is more attractive to a bowl than their current affiliated tie-in. I think it's reasonable to assume that the Big Ten, SEC, and Big XII will provide at-large BCS teams in most years, which gives the Big East at least a fighting chance to pick a bid off down the line.
I think the Champs Sports Bowl remains a pipe dream. Rutgers, USF, and Louisville on their best days don't approach the fan support of mid-level ACC teams, never mind any other pretenders. Even the sixth best Big Ten team seemingly holds more appeal. There's no chance of edging the SEC out of the Music City Bowl using any criteria, but an aggressive offer is at least conceivable possible vis-a-vis the fifth best ACC team. I'm not saying it's even likely, but it's possible.
Instead, I think the best option would be taking another crack at the Liberty Bowl. In 2005, reports indicated that the Big East was close to landing a bid for its #3 team, before a last minute concession by Conference USA to the SEC kept the bid in C-USA hands. That's life; when the Big East gets kicked, it picks itself up and goes to pick on an even weaker conference. Conventional negotiations might be enough to land the Liberty Bowl. However, if they're not, there is one other option. I don't believe that Memphis would add much if anything to Big East football, and has significant drawbacks in other areas. However, a potential sponsorship deal with FedEx and the lure of a Liberty Bowl tie-in are fairly enticing. It's just something to think about.
ACC:
Clemson - 81335
FSU - 80597
Virginia Tech - 66233
Virginia - 57732
UNC - 57417
NC State - 56356
Maryland - 51263
Georgia Tech - 50280
Miami - 43589
BC - 41990
WF - 32595
Duke - 20064
Big East:
Notre Dame (for the purposes of bowl affiliation) - 80821
WVU - 60400
USF - 53170
Rutgers - 43663
Louisville - 39881
UConn - 38205
Syracuse - 35009
Pitt - 33315
Cincy - 30246
Big Ten:
Michigan - 110264
Penn State - 108917
Ohio State - 105096
Wisconsin - 81747
Iowa - 70585
MSU - 70540
Purdue - 59326
Illinois - 54872
Minnesota - 51791
Indiana - 37004
NW - 24589
Big XII:
Texas - 85144
Oklahoma - 84858
Nebraska - 84501
Texas A&M - 82207
Missouri - 60232
Texas Tech - 51911
Colorado - 50509
Iowa State - 49462
KSU - 47383
Kansas - 46784
Okla St. - 40024
Baylor - 34378
Pac-10:
USC - 87476
UCLA - 76379
UW - 67732
Cal - 63136
ASU - 62875
Oregon - 58845
Arizona - 52161
Oregon St. - 41374
Stanford - 39332
Wash St. - 33045
SEC:
Tennessee - 103918
Georgia - 92746
LSU - 92619
Alabama - 92138
Florida - 90388
Auburn - 84689
South Carolina - 78467
Arkansas - 69707
Kentucky - 68824
Ole Miss - 49704
Miss St. - 49296
Vandy - 34629