Bikes on transit seems like a good idea, but the amount of space they take up makes them nearly impossible to work.
In order to pull it off you need extra wide doors, and extra long transit vehicles, so that they are always nearly empty and thus there is plenty of room on board for people to bring their bikes on, and it doesn't take too long. This is very expensive though and so nobody can afford to do that to their transit system. (Wheel chairs need similar accommodation, but there are only a few disabled people, while nearly everyone could bike: the scale of what is needed is different)
If you are serious about bikes as a last mile solution it is better to think of secure bike parking at transit stops so that people can ride to their local transit and park the bike. You still need to make sure the places most people are going is withing walking distance of a transit stop, but if transit is successful most stores and businesses will want to locate near great transit and so be willing to pay for TOD (if transit is bad they want to locate near busy roads). Thus we are mostly looking at people going from home to transit - when people visit friends/family they will have a long walk, but that isn't as common a trip (though bike rental looks like a useful option for this)