Buy a solid bamboo toothbrush, or an electric or manual brush with replaceable heads so the handle lasts for years. When a bamboo brush is done, pull the bristles out with pliers and compost the handle.
Four plastic toothbrushes a year at about 18 g each is around 70 g of plastic; the bamboo version leaves only about a gram of nylon bristle per brush.
The catch: most bamboo brushes still have nylon bristles, and any rigid, glossy bamboo-fibre product is likely a melamine composite; look for solid bamboo and a Plastic Free certification or clear material declaration.