I've actually run a stampede in my games before!

It was a herd of dire elk on the tundra for me (ah, the visuals of bounding, leaping, house-sized deer thudding around the party!), but the basic rules should work okay.
Roll initiative (but only for the party).
The stampede is continuous. The only hope to avoid it is to get to safety and ride it out. It is also over fairly quick.
As each party member gets an action, they must decide how they're going to avoid the herd on their turn. Possible options include trying to escape it, spend the round dodging bison, or finding the edge of the stampede and hoping to get outside of it. They might also improvise things (like using magic to turn the herd).
In NEXT, I'd use straight ability score checks: make a DEX check to leap up on the creature's backs and get swept along with them, or a STR check to scramble up the tree, or a CHA check to get the panicked creatures to turn aside from you. If the game is wahoo enough, a CON check might help your gnome barbarian just push away any bison that tries to trample you. If you're trying some complex spellcasting, maybe an INT or WIS check. DC would probably vary with the level, but I might sit it at something like 18 or 19 -- very very difficult for anyone who isn't already heroic in some way.
If you succeed on that check, for that round, you're safe (for this round).
If you fail that check, you take damage. I'd peg damage differently in different e's, but I'd peg it at "if this stampede hits a given party member every turn, what is the worst damage I'd want to inflict?" For me, that's usually character death, and a stampede that lasts about 3 or 4 rounds is good, so I'd peg damage as "enough to kill the highest HP party member in 3 rounds." In 4e, that would be conveniently pegged to damage in the realm of one healing surge.
I'd then have the stampede last about 4-5 rounds: I like the idea of a possible PC who fails three checks laying there in a heap bleeding out and having the other PC's have to decide between entering the herd to save her or staying safe and secure themselves. If the PC's are all hitting their checks and don't seem very threatened, I might end the stampede early.
So the threat is reactive, I'd make sure that whatever option the PC chose isn't safe. Trees get knocked over, grips loosen, hiding holes get blasted away, bluffs lose their effectiveness. They need to KEEP MAKING checks to survive. And different checks, too: find a tree that's knocked over, you're going to need to do something else in round 2. Blasting magic might work, but each round is going to consume a spell.
I'd expect this encounter to chew up a low-level party, which is fine: stampedes should be VERY dangerous!