CA glue (super glue) is a better choice in my opinion. Wood glue will work but CA glue has very little sheer strength. Which means that when you need to remove the nut (replacement, filing, reshaping, etc) all you need to do is give it a tap with a hammer and it will pop right off, leaving the bone and wood intact.
Wood glue on the other hand has very good sheer strength and sometimes when you try to remove the nut, the glue doesn’t break but rather sticks to the bone and what breaks is the wood.
With either glue though you only want to use two tiny drops. If you have squeeze-out then you used way too much glue.
I have seen people use Crazy Glue. The main reason I don’t recommend it to people I don’t know is because I don’t know their experience with using adhesives; If they get Crazy glue on the finish of the guitar, then they’re done. Almost impossible to fix.
Wood glue has much lower skill level entry bar Put too much on, wipe it off with a damp cloth. Easy. So the stress level is very low doing the repair that way.
This is a great point. Also you don’t really need anything to hold the nut the tension takes care of that already so if you need things to be in place add a very small amount. There’s no need to permanently secure the nut, you’ll have a difficult, very difficult time removing it, very, don’t ask me how I know this intimately, lol.
I use super glue too. It holds the nut perfectly, and it’s still so easy to remove when you need to. But what @Barney says about the finish is a good point for sure ! You better know what you do with super glue.
also if we talk about a 5 string bass, you’ll have 3 strings pulling one way and 2 other strings pulling in the opposite way, and the force won’t be equal so the nut can more laterally. a tiny bit of glue would fix that