I wear the "classic" Shock Absorber bra and you put it on exactly the way you put any other bra on. Try that one. I also found it the most supportive one for cycling although I don't believe any of the manufacturers really make a cycling bra. They tend to concentrate on stopping the up and down bounce of running but we all know that on a bike (particularly road bike) we lean forward... Which changes the dynamics somewhat.
I've never watched my tits when on the bike, obviously that would be dangerous, but I would imagine that if my tits were to bounce leaning forward, my tits would bounce in and out, rather up and down like when you run. However I can feel my tits bounce in a normal or underwire bra, so I always wear a sports bra. Coz once that damage is done... Only a nip and tuck will fix it... And I don't fancy having my nipples relocated!