There is a big difference between these two acts. The bowing means that you (and the country you represent)is inferior or below the one you are bowing to (placing the US subject to Saudi Arabia). Holding hands means working together as a team/group.
I think that’s because Michele Obama touched the Queen and put her arm around her (not exactly protocol towards a sovereign). To some, a Black woman touching a White Queen is an offense.
It was the putting the arm around.. it places the Queen as an inferior to Michele Obama (kind of what you would do to comfort/guide a child). And Michele Obama is not even a President/leader of state. This is what was the direct insult. The Queen of England has dealt and continue to deals with many black heads of state… without any insults either way.
There is a whole ‘protocol’ thing that occurs when dealing with heads of state.. it is really quite convoluted. ie: When in the presence of the King of Thailand, your head must be lower than his, but that differs if you are a head of state… then it is who grabs whose hand first, to they also do a grab of the forearm with the left hand etc…