I'm another non-car owning bike user. DD was in a Hamax bike seat until around 4, then we rigged up what we call our 'Frankencycle': a bike seat clamped to the parcel rack, footpegs clamped on the frame near the wheel hub, and a small set of handlebars clamped onto my seat post. Like a tandem, but with no pedals; obviously the rack has to be sturdy enough to take the weight.
She's now a large age 7 (98th percentile child) and is still using this seat. She also uses a trailer bike (could start from age 4 with a very, very trustworthy and biddable child who never falls asleep, but 5 is probably better) and a Follow Me Tandem, which clamps mine and her bikes together. She can ride a bike herself, of course, but we live in a hilly area with no safe roads for her to go solo on.
I'd agree that you'd first need to be a confident bike rider yourself before taking a 3 yr old out - try a bike seat with a large sack of spuds to get used to the weight and balance! You'd have to be comfortable and assertive about road positioning, the sort of rider who doesn't nervously have their seat set too low simply so they can sit in the seat and reach the ground (because by doing so you're getting nowhere near the pedal leverage you'll need to move a child around with you).
But I love taking the kids out by bike. So good for them; they're getting the Vitamin D even if they're not getting much of the exercise on the back, and they're internalising so much about roads and traffic that will be of benefit once they're driving. And it's lovely having a chat with the back seat driver as you pootle along.