Yes, BHO = Banjo Hangout
The BHO "players union" is simply a name given to people who support the BHO via donations...there's no affiliation with any trade or craft union. If you look down the left-hand side of the homepage, you'll see a clickable link to "Player's Union" (under "support this site", which is itself part of the Hangout Store). Clicking that "Player's Union" link will send you to the store where you can add membership donation to a shopping cart. When you check-out, it will give you options on how to pay.
Note, you don't have to be a member to enter the drawing. There's a page there full of information on the drawing and how to, etc.