Forgive my ignorance, but when did any angel accept worship?
Ooopse... Lot, not Abraham. Genesis 19. King James, oddly, translates the word as "bow," but in Hebrew it is the same word translated as "worship" in the decalogue. The King James bible frequently switches how it translates words so no-one catches the contradictions in James' politically motivated theology.
I would also note that John worships an angel in Revelations. The angel redirects him, so it's true that his action is not commended. On the other hand, John is in paradise, before the future throne of grace itself, having seen the Lamb of God in all His majesty; while the angel redirects his worship, it can hardly be supposed that John here has committed the grave sin of idolatry!
Again, John commits no sin. He worships before an angel whose will is the same as God's; it's just that John is (perhaps not quite grasping it at first) in the presence of Christ Himself.
To "worship" or "bow," however it is translated, connotes that the worshipper is placing himself in the service of the worshipped. Just as a soldier who bows before a Centurion has not turned his back on his allegience to Ceasar, one who bows before a servant of God commits no idolatry.
It should be noted that the Catholic faith does not permit praying to, or bowing before anyone who has not been recognized as a Saint. In fact, that is precisely why Catholics declare people Saint. It means more to Catholics than what Protestants take it to mean; it means that the person *recognized* as a Saint is certainly in Heaven, having united his will entirely to that of God's. Were this not so, the Catholic would sin. (And yes, some Americans have let some Protestantism rub off on them, and decided that they can know who is a Saint, not understanding what it means to be recognized as one.)
The one exception is this: In the performance of Mass, it is fitting that people should bow before the priest; the worship is not of the priest, but of the role which the priest is playing, representing Christ at the Last Supper. Again, this is why the AmChurch's liberal preists sin so gravely when they make themselves the focus of the mass; they rob the honor due only to God, and doing so confuse the congregation's understanding of what it is they are doing when they bow. Formerly, the priest used to stand before the tabernacle, holding within it the physical presence of the body and blood, soul and divinity of Christ in the flesh. Absent the tabernacle, it is less apparent that the people are bowed to Christ, and not the priest.