Water – Wooden window frame in shower

Since wood glues tend to be stronger than wood itself in my experience anyway, gluing the dowel to the board sounds like a solid plan to me with one exception...

I'd suggest reversing the order. Secure the dowel in the bearing first, since that step will put more potential strain on both parts. Particularly if the dowel breaks, you don't want it to be permanently affixed to the board when it does.

Compared to the force necessary to wedge the dowel into the bearing, the insertion into a hole in the board with glue in it will be trivial amounts of pressure.

If you can disassemble the frame, separate the siderails from the head and foot boards. Use a crayon or candle to wax the mating surfaces of the wood. This will help eliminate the squeeks. If the bolt has machine threads apply a small amount of thread lock (Loc-tite) which is available at the local hardware store. Get the smallest tube you can as you literally need four drops. One drop for each bolt. If the bolt has wood threads get some chair-lock. It is a glue designed for assembling chairs. Again apply a drop to each bolt. It also is available at the hardware store. While at the hardware store pick up the correct tool you need to tighten the bolt. Assemble the bed tightening the bolts until no movement is felt at the joints. If you can allow the bed to sit unused for an hour or so your adhesives can set.