I don't really know but they do level up.For example my ditto is on lv. 56 and when i left him there he was on lv.20
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Yes, Pokémon in the Daycare will still acquire Experience even if the steps you take are on a bike, they are still counted as steps.
It depends what level the Pokemon is. If it is a lower level it will take about ten minutes It a higher level it could take up to an hour
To level up Pokemon in the daycare walk as many steps equal to the exp. points required to level up. I would not use the daycare to level up because your Pokemon gain the minimum stats and your moves could be deleted for a crappy move.
Go to the pokemon center in Ecruteak City, Bill will come down stairs and talk to you. Then go to Goldenrod City to Bill's house and he will give you an Eevee. Get on your bike and ride around for 30 mins back and forth and fight some pokemon to gain a level, and if you ride around enough the happiness will grow and evolve. Better then fighting for hours trying to gain happiness.
Either put it in the front of your party and battle thousands of trainers or wild Pokemon, OR An easier way is to get the Soothe Bell and just run back and forth until you gain your pokemons Happiness. Every step while holding soothe bell makes it happier. And in HG/SS just walking with you also raises happiness. But don't let it faint or put it in your Box because it will lose all happiness.