Whether bowing to a monk, a lay Dhamma teacher, or a stūpa, why do you bow three times? It is because you are bowing to the Buddha, Dhamma, and Sangha (those Noble Ones who have realised nibbāna).
If you understand that your bowing is something done by you to show how much you respect the Triple Gem, and not how much you respect whoever is sitting in front of you, it becomes easy to bow, even to a monk or lay person who is weak in virtue, and far from the Noble Path.
It doesn't matter if the pile of bricks looking like a stūpa actually contains relics or not. Why should you allow that to affect your reverence for the Triple Gem? Nor does it matter if the person, photo, or statue you're bowing too is a Noble One or not. If your mind is purified by focusing on the qualities of the Triple Gem, that is what is important.
• • • • (Upasampadā: 24th June, 1979)