A bloody draw of sorts would mean that the Yorkists win. The Tudor Army was in enemy country, with a force mostly made up of French and Breton convicts and mercenaries, and while Wales had risen a bit for Henry, he had no real amount of English support until Thomas Stanley joined the battle.
The army would likely melt away or be driven back into Wales, where it would be contained. The Tudors HAD to win at Bosworth and win decisively, otherwise they would lose the campaign.
Now, this does bring up an interesting question, though. Who succeeds Richard? Its likely I think that Edward Warwick, son of George Plantagenet, is crowned King. The possibility of Yorkist pretenders certainly exists, and you probably see a continuation of the Rivers-Plantagenet feud.
However, if this draw is super bloody, it probably means that the best and strongest force remaining on the field was that of the Stanleys. The core of Henry's army, his foreign mercenaries and adventurers, are beaten to a pulp, as are Richard's men. But Stanley did not even attack with his entire force. That also means, however, that Richard's left flank, which also did not engage much, led by Henry Percy, is also intact. Perhaps what this leads up to is a Stanley-Percy battle to see who can become King by conquest, as neither of these factions were particularly all that loyal to the Tudors and Yorkists respectively and were trying to hedge their bets.
It is possible however that Stanley did not truly want the crown, and he would have rather tried to place his wife, Margaret Beaufort, on the throne, as Henry ultimately was basing his claim partially on her lineage from John of Gaunt (illegitimate though it may have been) and partially on being the half-nephew of Henry VI. This would be a weak claim, undoubtedly, but at that point, did it really matter? Nobody was going to take the throne without having to fight for it.
Really, this timeline needs more specifics on what happens at Bosworth (did the Stanley's commit their forces? Did Thomas Stanley survive? Did Henry Percy engage rather than avoiding battle? What happened to Jasper Tudor?) , as ultimately, who becomes King is going to depend on force of arms.