Kinsfolk Shop carries a range of wood brushes, including dish brushes with detachable heads from Make Nice Company and Redecker. These brushes are great because you can use the handle for quite a while and only change out the head when it starts to wear out.
(Just a quick note that the dish brush heads are not interchangeable between brands. The heads from Make Nice Company brushes don't fit on the Redecker handles and vice versa.)
The heads should last you quite a while providing they are cared for properly (letting them dry out completely between uses with the bristles facing downwards if possible, cleaning regularly, not letting them sit in water for prolonged periods). I usually get about 6-8 months use per head.
Once the heads have worn out, it's important that they are disposed of properly. It's simple to do and only requires a few steps!
Firstly, find yourself some pliers! Needle-nose work best.
Second, pry all the bristles out. They should pull out easily. If they don't, try boiling the brush heads for about 5 minutes in water. This will cause the wood to swell and the bristles should pop out easier.
Once you have all the bristles out, separate the metal staples. This part takes a bit of patience. If the staples are rusty, consider using gloves.
Lastly, once you've got all the bristles and the staples separated, you can now dispose of everything. The bristles and the head can go in the compost, and the staples can be recycled.
And that's it! You're done! Now just pop on a new brush head and you're good to go!