The story
From tooth + brush. Compare Saterland Frisian Tuskebäärsel (“toothbrush”), West Frisian toskboarstel (“toothbrush”), Dutch tandenborstel (“toothbrush”), German Zahnbürste (“toothbrush”), Danish tandbørste (“toothbrush”), Swedish tandborste (“toothbrush”), Icelandic tannbursti (“toothbrush”).
Etymology from Wiktionary, CC BY-SA 4.0.