There are a few quest mods out now that look like they would be really fun to play, like Falskaar, Wyrmstooth, Agent of Righteous Might, etc.

And as much as I want to play them I keep remembering something I've read somewhere before, that apparently even if you complete a quest they leave scripts running in the background and thus bloat save files.. is this actually true? Or is it a bit exaggerated, i.e. the save doesn't bloat all that much?

Here is what I do with quest mods. I create a forked save, and load up the mod, make a new save slot and play on. Once I am done with the quest, I archived that save, and uninstall the mod. I then load up the pre mod save and play on, or add another quest mod. This is for just about any quest mod for any game.

Now, I think this will give you the save that is free from scripts in this game. However, there is script extender command that is supposed to remove any redundant scripts from the save if necessary. I just don't have it with me.

Quests, modded or vanilla, have the potential to keep scripts running after you consider yourself to be done with them. This is not inherently a problem, unless said scripts are especially profligate (such as spawning new references and not deleting them.) Keeping a save prior to any mod is always a good idea, but I'd only roll back if you find an actual problem, rather than preemptively.

You are slightly misremembering:

There's only problems if you remove the mod and continue the same save game. Also, it's not just scripted mods (although they are the most noticed because the effects of removing them are pretty noticeable). It's the way skyrim itself works, it not the mod authors fault, the same problems will occur if you removed one of the official DLC. In fact one of the devs literally said "Skyrim does not support removing plugins".

What's happening is that when you run the game, various bits of data gets saved into your save files. If you suddenly remove one of the sources of this data, Bad Things™ will follow.

Best approach to modding in general: Before installing mods, make sure you make a separate save. If/when you decide to remove it, you revert back to that save that never had the mod loaded. Otherwise, stick with your load order until you retire that character (you can still add mods, just never subtract)

- Hypno

Sounds good, so as long as I don't uninstall the quest mod all is good? So I shouldn't end up with a large bloated save file if say, I finish with Falskaar and then move on to Wyrmstooth without removing Falskaar, right?

Also, it is entirely normal behaviour that your save file grows larger over time. It does so by simply playing vanilla Skyrim, and if you add mods, more things get added to your savegame. That's nothing to worry about.
"Bloating" a save is quite easily noticeable - it refers to your saves growing by several MB during a half hour of playing, or getting 60 MB save files, or things like that.
So mods will increase your savegame size; they will, however, not "bloat" it. Except if they're really buggy (and of the well-known quest mods, none are), or if you remove them from your mod list. As a guide line, never ever remove a mod from a save.

Edit: Yep, exactly. Just leave Falskaar in it; it doesn't do any harm.

Nice! There's several quest mods I've always wanted to play! Thanks for all the input!