I started the year with 3 toothbrushes (one for travel, one for home and a third new one from a multipack waiting until it was needed) so I had plenty of time to search for alternatives before I ran out, unfortunately it is slim pickings out there, bamboo toothbrushes well publicised but seem to only come in a box, with a layer of something else inside and any I have found have "biodegradable handles" written on the box, which to means that the bristles are not biodegradable!
I was very excited when I bought a wooden toothbrush with pig hair bristles in minimal packaging, but after brushing with it once the head looked like I had been using it to clean the grout between my tiles for years, I am embarrassed that visitors will see it in my bathroom and I don't feel that it cleans my teeth as well.
I am considering throwing it in the compost bin and going back to my old plastic toothbrush, but this isn't a permanent solution because although my toothbrush may last a very long time in landfill it isn't going to useful for very much longer!