Locate a Recycling Collection Center That Accepts Bicycle Tires/Tubes
Locate a recycling collection center in your community that accepts bicycle tires. If you live in a large city this should not be a problem as most big cities have a tire recycling plant that will accept bicycle tires and tubes.
You should be able to find one with an Internet search including the name of your locality. Then take your bicycle tires/tubes to the plant you located.
Get Creative About Recycling Bicycle Tires/Tubes
If there is not a tire recycling plant in your area then collect and ship your used bicycle tires and tubes to a tire recycling plant in another city.
This option can be expensive, but you can ship more economically if you collect tires/tubes until you get a couple of boxes full (you could even consider a bicycle tire recycling drive for your community) and then ship them.
Also consider putting the boxes in your trunk and dropping them off when you are traveling to a nearby city with a tire recycling plant.
Reuse your old bicycle tires/tubes. There are several business that will accept your old bicycle tires and tubes and reuse them to make flip-flops, parts of chairs etc.
If the tires and tubes are not totally worn out (punctured but patchable is ok) there are a number of non-profit organizations in both the U.S. and Europe that collect bicycles and bicycle parts to ship to third world countries.
Or you can use your old bicycle tires and tubes in your own community for do-it-yourself-projects or crafts. Some crafters make handbags, shoes, lawn furniture, sculpture and other interesting and unique items out of old bike tires and tubes.
Costco retail outlets will accept old bicycle tires/tubes for recycling in many (but not all) communities.