My city has a recycling center for household products, but it requires the use of a motor vehicle. I have been unsuccessful in using taxi or ride-sharing services to drop off items. Unfortunately, the inflexible vehicle requirement is a deal breaker for me and many of my neighbors.
Some recycling centres in my country don't allow entry on foot. They'll allow entry on a motorbike, don't know about a bicycle.
I speculate it's because they often have hours-long queues, and people in cars might decide to park and walk past the queue, if it was allowed, which could get chaotic.
Or perhaps the rules were just written by someone who hadn't considered non-car-owners.
In Norway most supermarkets have a box for used batteries, broken light bulbs, fluorescent tubes as well as a reverse vending machine for drinks cans and bottles.
Shops that sell electrical goods (computers, audiovisual, cookers, etc.) have to be willing to accept electrical goods for recycling even if they don't sell that specific model or even brand. So a lot more people are within a reasonable distance of a place to recycle quite a few things.
A lot of them also do curbside recycling once or twice a year for electronics and large appliances. Mine does, but I don't like batteries sitting around where I'll forget about them and my local dump is right across the street from a Home Depot, so I drop them off when I usually go to Home Depot.