The phrase "bulky stroller" refers to a stroller that is large or takes up a lot of space. It suggests that the stroller might be difficult to maneuver or transport because of its size. Full definition
However, you don't have to have the big bulky stroller if you still want a travel system. (stroller-envy.com)
This means that just because you have twins or two smaller children, you don't have to worry about only traveling around with a large bulky stroller. (earlymomentsmatter.org)