If your really serious about a 350 class bull then I'd recommend talking to Carter's Hunter Services. Their website is huntinfool.com .
They know all the top area's and work with the top outfitters. membership is $100.00 but if you want big critters than its money well spent. Those guys are great to talk to.
Getting a tag is the tuff part. If you dont have points built up to draw then best bets might be New Mexico or Utah where you can hunt with a landowners voucher for a little cash. On a fair chase hunt there are no sure things on getting a big one but some hunts at least offer a sportin chance.
Occasionally a huge bull will be taken on a general tag in Wyoming in the wilderness area's but a 350 " is the exception to the rule. In 07 I got a 360" on one of those hunts but mostly bulls run from 300 - 320
Another option if you have cash is buying a Wyoming Commisioners License where you can bypass the draw system for a permit. Those normally go for 8-10K and may be a tax deduction because they benefit non- profit orgs.
Hope this helps