A public transport-friendly, which means light enough while not too robust pushchair, will always be a stroller compromise when it comes to bumpy roads, cobblestones, etc. I will suggest reading our short guides about stroller wheel types and stroller suspension to understand that more, but the general info here is: the larger the stroller (and its wheels) the better on bumps and holes it will perform... but the less it will be suitable for buses and so on, as it will be larger and heavier.
In here, I would most certainly suggest a lighter option with an OK suspension, while you should be counting on the fact that the bumps will be felt a bit at least. My own choice here was an Babystyle Oyster Zero which is a wide-seat, nicely shock-absorbing pushchair with a VERY large hood and a pretty much lie flat... clocking in about 7.2 kg. I was happy with it even on grass. There's no adjustable handle but the pushbar's height was actually rather nice and I don't think you'll suffer using it at that height.
Next in line would be a Valco Snap or, if bumps are truly a priority, a Valco Snap Sport with air filled wheels (they will act instead of the suspensions). Still rather light, and without an adjusting handlebar, but still very suitable for your needs, I believe. The weight here being the biggest advantage, and the stroller's price OK.
If you have a TFK Dot 2 or a Gesslein S4, these should be also good, capable options.
Kinderkraft and similar brands are, I think, OK even with the few not-the-best reviews because there, the priority is the price. I think for normal urban terrain and not too demanding parents, even the Kinderkraft Grande could be fine - just don't expect too much...