When you say 'network'
are you asking for the 'best' bingo site out there or are you asking for the 'network' that has the most sister-sites?
The best and only bingo site I recommend is BingoMania.com as they have the most rooms to play in at different costs for each, NO playthrough rules for bingo OR casino games, use software to stop you from using bonus bucks to play casino games so no there is never a question about money won, each room has its own progressive jackpot, each room has its own hourly (sometimes twice hourly) coverall jackpot game, has set game schedules for each room starting at 10AM EST, great, knowledgeable, helpful chat hosts in each room, gives almost immediate responses to help tickets (no live help), and has a player membership that is almost always consistent with a large number of them playing in chat so when you look at the number of players playing vs the number in chat you will see very few are in the lobby. You can play multiple rooms at the same time easily, you can use a downloaded version or website flash or even both at the same time. Deposits and cashouts are quick and easy. I've been playing there for nearly two years and have yet to see a chat comment made where somebody is unhappy...problems are immediately answered by the informative chat hosts or the host will actually check while the game is being played to get an answer...sometimes that answer needs to be diverted to a help ticket but most times, the host resolves it within chat itself for that player.
I can honestly say that with all the sites I've tried out, Mania is the ONLY site I recommend if you are looking for an honest and fair place to play at.