species of bean, piper longtum
蓽 refers to a specific plant: a species of bean or the long pepper plant (piper longum). The two meanings are distinct botanical items, so the core idea is simply a particular kind of plant.
蓽 combines the grass radical 艹 with 畢, which likely provides the sound. The character was created to name specific plants.
The grass radical 艹 sits above 畢, like a plant label. Think of 蓽 as a grassy plant with a name that sounds like 畢.
For ヒツ, imagine a plant that grows in fits and starts: fits -> ヒツ, and this bean plant sprouts in sudden bursts.