My board has 145 registered members, 4,000 threads, 40,000 posts and a 70MB database and this month so far I have used about 4GB of bandwidth. I gain about 2-4MB in my database per day; since June is almost over, you probably won't need more than 1 or 2GB of bandwidth based on my own board, but I guess that depends on the BB software you use, UBB screwed me good on that one, since my old host cost $10 per extra GB you went over each month (I went over about 4GB for 3 months), then I bought a license for and switched to vBulletin.
I guess there are many factors here to deal with. Does the site do anything else? What type of banner/ads/other graphics exist on the forum? What amount of posts there are. Are people doing a lot of reading or constantly opening and closing threads. As you can see there is no easy answer. I am hosting a site for a customer that has about that usage and It will probably be in the 40-50G range....cost for hosting $25-35.
0.75 without Avatars and Sigs, 1.5 WITH Avatars and Sigs.
With proper tuning of the DB and MySQL engine, wise gzip use and no Avatars and Sigs or Attachments you can go as low as 0.4-0.5GB and even use a FreeHost that supports MySQL. If he doesn't you can use f.e. IKONboard which has his own file-system based DB system.