"Fortunately I could get into the next bus" vs. "fortunately I managed the next bus"

A native speaker of English would be unlikely to say either. You might hear instead:

Fortunately, I was able to [or managed to] catch [or get] the next bus.

Both are grammatically correct, but as previously noted, neither is likely to be heard from native speakers of English. While sentence (1) is particularly unlikely, it certainly could occur in the conversation of some large person talking about a bus too small for them to fit into. A conscientiously-brief speaker might say (2), but either of “Fortunately I managed to catch the next bus” or “Fortunately I caught the next bus” is more likely.