Male / Female bow etiquette

I am headed to Japan for the first time. I have read many tips for Americans in Japan. I will be meeting with Japanese families and business people. My question is if I meet an older Japanese couple is it proper to bow to the husband ( male ) or wife ( female ) first? Or am I over thinking this. Any thoughts welcome. thank you.

There is no specific gender priority in bowing. The order is just as how it is in the international world. You typically bow to the first person you are introduced to or the first person you spot.

But of course, if you're trying to sell something, that may be another story. Depending on what you are trying to sell, you might want to make the women feel better or you might want to make the men feel better. I don't think it's a Japanese thing though.

I am a Japanese. In business meetings we always shake hands with non-Japanese. We do not expect non-Japanese to bow, though if you do, it surely would make us see your sincerity trying to respect our culture.

When you meet Japanese family, I guess it is not a formal ceremony... if they are old - say over 70 years old and they have little experience of meeting with non-Japanese, bowing would be nice. But they would also be pleased to shake hands with you too. Greeting to the host first would be the manner. But we all know about "ladies first" in Europe/America, it would not make big problem.

In conclusion, my advice is "Do not worry too much" Your cordiality will naturally be passed to them by your attitude anyway.

"In business meetings we always shake hands with non-Japanese. "
That's really not true at all...
It might be a bit more common with visiting non-Japanese as opposed to residents, but still.

My experience matches with GattoNegro in that when Japanese interact with non-Japanese, especially in a business setting, they almost always expect to shake hands. That said, bowing is a nice touch, although don't be surprised if they still try to shake your hands.

You know, I think I understand the original question more clearly now.

When you shake hands, you need to decide who to shake hands with first, because you can do hand-shakes with one person at a time.

But when you bow, you tend to bow to all the people present. It's more like waving or smiling, as opposed to shaking hands. You don't really have to decide who to wave, smile or bow to. And then when someone says something more specific like "This person is so and so." then you might want to bow again directly facing that specific person, just as you might smile again to that person.

And as mentioned, not every Japanese is used to shaking hands, so it would be a nice gesture to bow even though the Japanese you're meeting might think it's a nice gesture to shake hands with you.

No need to do bow if you are a international visitor.
No need to handshake as well.