Translation:I can no longer ride this bicycle because it is too small for me.
The Czech "na" is a red herring, different languages use different (if any) prepositions. For English compare https://books.google.com/ngrams/graph?content=ride+a+bike%2Cride+my+bike%2Cride+the+bike%2Cride+on+a+bike%2Cride+on+my+bike%2Cride+on+the+bike&year_start=1950&year_end=2019&corpus=26&smoothing=3
To me (native AmE) "I can ride this bicycle no longer..." sounds odd, as does the "I no longer can ride this bicycle..." option referenced in an earlier comment. Neither feels completely wrong, just somewhat unusual. If "I no longer can ride this bicycle..." is now accepted, perhaps your suggestion can be added as well.