Maggie, I didn't realize Bjorn was one of O Sensei's first generation Japanese student. If it's so, forgive my ignorance.
But even if that was the case, what exactly does bowing have to do with a gendai martial art; maybe your effectivenes applying techniques will improve, or will it be that your inner self will get closer to enlightment.
Of course, your O Sensei's deshi, his rules. You won't see me training with them, there are many many fishes in the water.
I'm not talking about Bjorn. I'm talking about advancing in Aikido beyond the weekend hobbyist. Anyone who is serious in Aikido, will at one point seek out O'Sensei Deshi, whenever they can. When it comes to that point, bowing might be in order for the sake of social politeness.
If you are just a weekend Aikidoka, and being half way decent for your local dojo is good enough for you, then it doesn't matter. Bow or don't bow. But don't show up for Chiba's, or Yamada's, or what have you's class and be disrespectful.