The headword Bosor, which appears in that form throughout the Septuagint (beginning with Deuteronomy 4.43) and also in e.g. the New Testament (2 Peter 2.15) and Josephus (Antiquities of the Jews 12.340), should more accurately be "Botsor", a variant of "Botsrah", the town בצרה of the Edomites that was destroyed with great bloodshed, leading to the image of God as a warrior dripping blood after having "trodden the winepress of Botsrah".
Cyril of Jerusalem (Lecture 13, paragraph 27, at web address 1) apparently did not understand the reference and decided that "botsor" must mean a red garment:
"Again, when He had been judged before Pilate, He was clothed in red; for there they put on Him a purple robe. Is this also written? Esaias saith, 'Who is this that cometh from Edom? the redness of His garments is from Bosor' (מבצרה; Isaiah lxiii. 1, 2.); who is this who in dishonor weareth purple? For Bosor has some such meaning in Hebrew. 'Why are Thy garments red, and Thy raiment as from a trodden wine-press?' But He answers and says, All day long have I stretched forth Mine hands unto a disobedient and gainsaying people."
For "scarlet" see LSJ s.v. ko/kkos, II (literally the berry or gall of the Quercus coccifera, used to dye this color; see e.g. Pausanias 10.36.1-2).