I wouldn’t use carpet tiles, they’ll end up sodden, but AstroTurf might work.
What’s the floor of the shed? My suspicion would be that you put a wet bike in, the water drips off, forms a puddle,.that evaporates, condenses, you put the bike back in wet the next day, etc, etc.
Ideally I’d suggest finding a way for the condensation to drain out of the shed after it’s run down the roof/walls. If puddles form anywhere, drill some small holes?
If not then the only real solution is ventilation and more of it. Could you hook up a small 12V solar panel and a computer fan so that when the sun does come out (and the water is evaporating) it’s blowing the moisture out.