Learn Italian: Non si entra senza bussare. - One does not enter without knocking.

In Italian, when you express 'without doing something', you use senza followed directly by the infinitive. This is called an implicit clause, and you use it when the subject of both actions is the same. Here, the generic person who wants to enter is the same person who needs to knock.

English uses an '-ing' word ('without knocking'). Why doesn't Italian use the gerund bussando?

After prepositions like senza, di, or per, Italian always requires the infinitive form of the verb (like bussare). You cannot use the gerund (the -ando or -endo form) after a preposition like you do in English. You have to think of it literally as 'without to knock'.

What exactly is si entra and who is doing the entering?

This uses the impersonal si construction, a very common way to state general rules. It does not refer to a specific person. Instead, it means 'one', 'people in general', or the generic 'you'. Therefore, non si entra means 'one does not enter' or 'you are not allowed to enter'.

Could we change the word order and put senza bussare at the beginning of the sentence?

Absolutely. You can safely say Senza bussare non si entra. Moving the senza clause to the front simply puts more emphasis on the condition of knocking first.