No. It has nothing to do with the English.
The choice of preposition is always confusing. Why are you sleeping on a bed but sitting in a chair? Why do you swim in the sea but driving on the road? Even worse: you can find sources for sailing in the sea and on the sea. This is the same in any language.
So in Hebrew you sit על a chair, you drive ב road, you swim ב sea, and you sail ב sea but על the water. As for a bed, you'll find both ב and על, but in my opinion ב is far more common:
היא ישנה במיטה שלי
I am not aware of any case where על translates to "to"