This isn't another take on the pink letter.
I've never been much of a writer. Apoligies for what you are about to read.
Show killed him fighting near Winterfell and made Jon win the BoB so that's two "major" battles against Boltons in the show but that's not neccesarily so; because Stannis didn't even get a few mins of battle while Jon had the majority of run time of an episode named after his battle so while it is supposed to be two different battles, it is actually one, run time wise.
Show always adds, cuts and merges characters, events, storylines etc.
So, I think we will only get one battle against Boltons in the books, the one Stannis is leading. Here are a few more supporting reasons apart from the above:
1) Jon has no army; before Stannis left the wall Jon had 200-300 fighting men among the wildlings, which he kept in exchange for 2000-3000 hill Clansmen, he has what few Queens men remained in Castle Black, his brothers of the Watch, which was around 1000 strength inits entirety even before the great ranging and Mance's attack took their tolls.
2) While Jon has no troops to fight a battle, let alone a war Stannis has managed to build himself an army out of whoever still remained available on the western half of the North, so not only he has an army but he and Roose have splitted whatever troops remained in North between themselves, after their war against each other ends there won't be any troops left for anyone else to wage war.
While I'm at it, I'd also like to take a look at Stannis' military situation: he sailed North with less than 1500 men and though it was light he nevertheless took some casualties (mammoth smashing one of the cavalry columns) against Mance. After the battle he's outnumbered 5 to 1 against Boltons but with Jon's help he now has more than 5000 men, with the possibility of adding some 400-1200 more (800 Umbers and what remained of their 450 strength levy after Stannis arrested the Karstarks) compared to Roose's possibly less than 7000, excepting Manderly and Locke and whoever else came later on, so though he has no horse remaining and hill clansmen not being so good battle troops, numbers are still rather balanced, especially considering Roose chose to sit back while sending Ramsay, Freys and Manderly to battle Stannis.
And one final piece of information; though she misinterprets (or maybe they are just open for misinterpretion) what she saws, Melisandre's visions always (almost always?) comes true, and before sailing to North Stannis discusses how he saw a king, whose crown was burning him.
With all the above taken into consideration, I think Stannis will come out as the victor in the battle with Ramsay. So if he's survivng this battle, how will he die?
Because he's the king that Westeros deserves, but not the one it needs right now. So we'll fight him, because he can take it. He is a teeth gritting guardian. He is pure iron. A truly just man.