I guess it really depends where you are biking as well... out on trails or around town? The chest pack, though not full on tactical, still kind of screams gun, at least a little, but I think it would be your fastest access while biking. If you are trail riding and you pop around a corner and find a sow with some cubs and she decides not to run a way, it may be nice to have some quick access to the .45.
(Please note that I would never advocate carrying anything less than a .44 mag if you are out in known bear country and have a strong likelihood of meeting a bear, but if your .45 is all you have, that is much better than nothing.)
For now I'm mostly riding around trails in town. My main concern while biking are the two legged threats. There is a possiblity of bears, but I'd assess that risk as low to moderate. When I'm in bear areas hiking, rafting, hunting, etc. I've got a .44 that I open carry in a leather chest mounted holster that works with a backpack on and is really fast to draw from. I agree that a .45 against a bear is better than nothing, but that better not be "Plan A."
For carrying my .45 around town I do like the quick access that a chest pouch offers, so I'll probably go that way. It will scream (or at least whisper) gun, but for quick access I'll accept the tradeoff. Besides Alaska is a pretty gun friendly state. Most people that would recognize the chest pouch as a concealed carry holster probably wouldn't care much.