Susprised there isn't a thread for him already, but anyway here goes. This is gonna be more of a random musings than an actual guide, once the wiki is back up i'll write something more coherent.
Bison is an upper mid to top tier character. He does loads of damage, has some great normals, awesome throw and has few bad matchups. Despite his good points his he is a tricky character to use. With only his super as a reversal, your opponents are gonna put a lot pressure on in the air and in the corner aswell as on wakeup situations.
Bison has to take control of the match. Your main aim is to get a knockdown. He has alot of options after he knocks down an opponent (remember if your going for a meaty/tick attempt, then slide in after the knockdown to close that gap asap while keeping your charge):
-Crouching Forward is a beastly meaty, incredibly hard to reverse. You can score big combos off it or tick in throws. You could try comboing into scissor/crusher or ticking straight into throw or link a short or two into a throw. Even could try cancelling into a headstomp to mix things up a bit. In the corner a meaty blocked crouching forward cancelled into a crusher will cross up the opponent ready for a combo or throw.
-Tick throw with standing short or standing strong. Once again hard to reverse.
-Cross-up Roundhouse/Forward, allows for combos and standing short pressure and ticks. Example combo would be crossup roundhouse, standing short x2, crouching forward cancelled into a crusher. If blocked go for a throw after the first or second short.
-Headstomp and devil reverse are good attacks on a downed opponent which has a number interesting follow ups, such as walk in throw. standing strong also combos with the punch followup of the headstomp and dizzies quite often.
-Meaty super, good for finishing off opponent by chip damage or can setup some good pressure such as tick throws or added block string chip damage.
Bison's Throw is one of the best in the game, allows for lots of ticks and has lots of followups, regardless whether the opponent teched it or not, abuse it as much as you can. If opponent techs the throw you can walk up to them as they land, and tick into another throw with standing short. If they get used to that then walk up, crouching forward into standing Roundhouse combo. If they don't tech refer to the section above. Also if you manage to throw your opponent into the corner you can try a slide which ambigiously crosses up in the corner.
Even with a lack of reversal, bison does have some anti-air options. His Jumping Strong has alot of priority and combos into more strongs whilst in the air. Coupled with his incredibly long jump, as long as you can see the the opponents jump early you should be able to beat nearly any air attack. Straight up jumping forward/roundhouse also works extremely well. Also Jump straight up Short works well to hit sim's limbs on the way down. And at certian ranges scissor kick will also do the job.
Bison's standing forward/roundhouse is good for stuffing and trading with fireballs, aswell as following up a blocked scissor kick. Bison can do some serious chip damage in the form of block strings, nowhere near as good as champion edition days but still worth mentioning. Using scissors and jab crusher coupled with crouching forward, standing short, standing forward and standing and crouching strong you can make some interesting block strings to confuse and expose your opponent. Avoid extended block strings as these are reversal bait.
Combatting fireballs its best not to jump in, his air time is long so easy to anti air, so i suggest jumping straight up over fireballs and gradually walking forward and put some pressure on with your forward and roundhouse. Be prepared to jump mp on reaction though as opponents may try jumping at you if you get with their jump range.
Some combos you should try to learn are, obviously your jumping strong combo in the air. Try to land one, and jump again to get the other 2 (max 3 hits in total) when you have super. As you combo the super on their way down after the 2 hits.
Also jumping roundhouse, crouching forward cancelled into crusher is good damage and dizzies alot.
TOD (touch of death; does over 50% damage and dizzies) combo is jumping roundhouse, standing short, crouching forward cancelled into scissor for the dizzy 99% of the time.
Also the crossup cobo explained above, if its too tricky, try jumping crossup roundhouse into 2 standing shorts followed by a standing forward, not as damaging, doesn't normally dizzy but easy to do.
Thats all i can think of at the moment, hopefully some much wiser players can contribute.