If you wish to avoid "fancy chemical mixtures that I don't understand" and use water-based glue, then don't be surprised when your frame disintegrates when you are riding your bike and it rains.

On the other hand, if your bike to last beyond the next rainfall, then I would also recommend using West brand epoxy. It is what I used for my wooden bike.

There are several kinds of West epoxy you can use: The first kind is resin/hardener. You mix two and half parts resin to one part hardener. It stays workable for 45 minutes, then hardens. You have to clamp the pieces together until the epoxy cures. It takes 24 hours for the epoxy to cure at 70 degrees F. If the temperature drops below 60 degrees F, then the epoxy won't cure. I used 105 hardener/206 resin. When it cures, it is stronger than the wood.

The other kind, which my friend recommended, is G/5 epoxy. You only have to hold the parts together for 5 min. It cures in 5 min. I did not try this because I thought I might not be that quick.

When the epoxy is cured, it can be sanded, drilled, filed -- just like wood.