" 'Amazingly rare' letter written by Robert the Bruce to Edward II found"

[Dale Seago]

Didn't manage to put off the battle of Bannockburn though. And who won that?

If you're talking about the battle, purely as a single engagement, it seems pretty clear:

Edward fled with his personal bodyguard, ending the remaining order in the army; panic spread and defeat turned into a rout. He arrived eventually at Dunbar Castle, from here he took ship to England. From the carnage of Bannockburn, the rest of the army tried to escape to the safety of the English border, ninety miles to the south. Many were killed by the pursuing Scottish army or by the inhabitants of the countryside that they passed through. Historian Peter Reese says that, "only one sizeable group of men—all footsoldiers—made good their escape to England."[9] These were a force of Welsh spearmen who were kept together by their commander, Sir Maurice de Berkeley, and the majority of them reached Carlisle.[9] Weighing up the available evidence, Reese concludes that "it seems doubtful if even a third of the footsoldiers returned to England."[9] Out of 16,000 infantrymen, this would give a total of about 11,000 killed. The English chronicler Thomas Walsingham gave the number of English men-at-arms who were killed as 700,[7] while 500 more men-at-arms were spared for ransom.[27] The Scottish losses appear to have been comparatively light, with only two knights among those killed.[28]
(http://en.wikipedia.org/wiki/Battle_...ckburn#Retreat)

If you are thinking in terms of a "larger" historic sense, I think your query would be better applied to Culloden -- I believe things would have gone very badly for Scotland afterward regardless of which side won the battle, and for that matter the war.