This word presents something of a melange of flavours. The pic naturally brings to mind a point or a sharpness, whether from pick or pique or piquant, and the picro in full reinforces this with a hint of, for instance, pico de gallo; the cr has that grasping, gathering, grabbing feeling to it; the ror more rolls than roars on the tongue, and is, like rural, a bit of oral effort to say because it quite lacks any points of clear opposition, just a rolling subsiding and resurging of the tongue; the rh we know is just another /r/ but gives the visual effect of a wheeze, reinforced by the iz; crorhiza may make a person think of coryza, also known as catarrh but commonly called runny nose today. Put together it may seem a bit like the various rumblings and groanings of unhappy innards. Visually there is also a certain sense of smoothness in symmetry, in the _i_ror_i__, but disrupted by sharp and unbalanced p c h za.
But does it taste bitter anywhere in the root? Well, it has a bitter root (but that root is not bitterroot, which is a nameused fora few other plants, significantly Lewisia rediviva and also, according to the OED, Apocynum androsæmifolium). Specifically, picro is the Greek root (typically a prefix in English) meaning “bitter”. It happens to be used nearly not at all in ordinary English, reserved for taxonomic terminology and similar scientific usages. On the other hand, rhiza does show up a little in common English, mutatis mutandis, for instance in rhizome. What is it at root? “Root”, in Greek of course.
So picrorhiza names a bitter root? Yes, specifically Picrorhiza kurroa, a plant called variously katki, katuki, kutki, or katuka. It grows in the Himalayas (I know not whether it grows in a row on the peaks, but that would seem to lack reason, because Himalayan peaks are rather inhospitable to vegetation; however, it does grow at high altitudes); it has been used medicinally for ages as a treatment for heart and liver problems, jaundice, and asthma. It would appear that such other botanical names as mycorrhiza as well as its medical context, bringing with it recollections of words such as arrhythmia, lead it sometimes to be written picrorrhiza, which is nonetheless a misspelling. Its active ingredients include picroside I, kutkoside, androsin, and apocynin. Research indicates that, among other things, it protects the liver and stimulates bile production; it may also help the immune system and may lower blood sugar. And – and this is fortunate – it appears to help treat hypoxia. So if you get altitude sickness while up picking it, you could always eat some. But watch out: it’s quite bitter.
Thanks to Dawn Lowen for mentioning Lewisia rediviva and mycorrhiza.