As far as bowing goes, in our dojo at least its made
very clear that it's just a formal greeting. In Israel, with
a lot of orthodox Jews and Muslims (yes, we do
practice together) its an important point. For the same
reason there is no clapping at the beginning (its a
Shinto cleansing/summoning ritual). People take
their religion seriously here...
What may be of more concern, and no-one's mentioned
so far, is a Ki-Society dojo that explicitly talks about and
works with the existence of ki - universal energy akin to
the 'Force' from Star Wars (ducks and runs).
This seems to cause the biggest problem for Christians,
and I know of one dojo in the UK which had to move from
the Church hall it was using when the priest saw the class
and heard what was being said (he also kicked out a Tai
Chi and a Yogo class).
Other styles (Aikikai, Yoshinkan) usually either don't talk
much about it at all or use it as a metaphor for relaxed
movement. Incidently this is probably the biggest split
in modern aikido.
You may want to ask your local dojo what style they practice
and their attitude towards ki.
Also incidently, O-sensei was not a Christian, knew little
about Christian teachings but was interested in it. He was
once asked how aikido fitted with the principle of turning
the other cheek. He was at first puzzled, and when the
story was explained to him said that aikido was very similar,
but in aikido we turn the other cheek before they hit us.