A confilict between bowing and religion is somtimes a crucial aspect of why people are uncomfortable with bowing but I think that sometimes there are also some cultural attitudes that are different between Japan and western cultures (including the US). Some of this has been touched on in others' posts, but I thought I would clarify it a little more.
In Japan, bowing is a complex social activity which communicates many things including the social standing of each of the participants and the amount of respect that the bower has towards the bowee (heh, new word). All this is lost on many of us westerners. Even if we have spent some time in Japan, it is often difficult to really understand the dynamic that occurs between Japanese people, symbolized by a bow, since that dynamic is foreign to us.
On the other hand, some westerners (including Americans) tend to think that bowing to a person, especially the low bow that we do before class, means that the bower is expressing his/her inferiority. We have heard stories of the kow-tow, where subjects bow to emperors and such, demostrating their complete inferiority to the emperor. Of course other types of bowing occurs in western society, but none of them are so ritualized as what we do before class. This sometimes leads to a misunderstanding of what peoples' intentions are when they perform a bow.
Perhaps if you tell visitors who are uncomfortable with bowing that it is a non-religious activity, which is just meant as a sign of respect to the founder of Aikido. Or tell them what I think of when I bow to O'Sensei's picture: I thank him personally for having had the insight to create such a beautiful art, and for teaching it so that I could learn it. In this way, I don't consider it bowing to a picture at all, but bowing to the memory of O'Sensei and being grateful to those who have gone before and played a part in my training.
Now if a person's religion gives them a specific meaning to bowing (such as the examples of the Muslim Judoka or the Aikidoka in Jerusalem), then that is a totally different thing and should be respected. If the reasons for not bowing are just cultural misunderstandings, then I think they should be clarified at least. Then the visitor can make up his/her own mind.
Wow, that turned out really long
just my (long) opinion,