You can still pick up Candies and hatch eggs on the bike, but it's slower. This is a conversion chart detailing the speeds over the various bots, and their conversions.
Walking 3.6 km/h = 2.237 mph = 1 m/s
Egg/Buddy distance tracking limit 10.5 km/h = 6.5 mph = 2.9 m/s
Jogging 10.8 km/h = 6.711 mph = 3 m/s
Ideal Incense Travel Speed 15 km/h = 9.3 mph = 4.15 m/s
Ride a bike 21 km/h = 13 mph = 5.8 m/s
Passenger Warning Threshold / Pokestop Speedlock limit 30 km/h = 18.6 mph = 8.3 m/s
Pokemon Sightings & Encounter limit 48 km/h = 30 mph = 13.4 m/s
Softban speed limit (Insta Break & Run) 100 km/h = 62 mph = 27.7 m/s