I have the same strategy of exploration except I do it by running. I recently moved to Prague and my way of learning the city layout is to look at a map and plan a rough route that connects certain landmarks and then I go out and try to run it by memory. Rinse and repeat and pretty quickly and I quickly end up knowing the city layout better than almost everyone including the locals. The only issue with this approach is that you naturally end up knowing your are much better than the rest of the city, but even that can be helped by starting out with a tram ride to some other part of the city and then running back.
That said I like doing this both by bike, tram/metro, _and_ by car as well. By bike it's the same process, but you see everything faster and take different routes. Riding the tram/metro connects you to places in other ways and kind of teaches you those routes. By car it's the same thing, but another level. For me the important part is to basically not look at any map throughout the process and find your way around by landmarks, signs, etc. Looking at a map before/after is fine, but during you should just be navigating own your own.