Mi veturas per biciklo al la biblioteko.

Veturi means to travel / ride / go by means of a vehicle or conveyance. In this sentence, the speaker is not just going somewhere; they are specifically traveling by bicycle.

Iri is more general: Mi iras al la biblioteko = I’m going to the library, without saying how.
Mi veturas per biciklo al la biblioteko adds the idea of transportation.

Esperanto usually uses per to show the means or method of transportation.

So:

per biciklo = by bicycle / using a bicycle

English often uses on for bikes, buses, trains, etc., but Esperanto does not usually copy that pattern.
Sur biciklo would describe the physical position of being on top of a bicycle, not the normal way to express the mode of transport.

Per means by means of, with, or using. It introduces the tool, method, or instrument used to do something.

So here:

Mi veturas per biciklo = I travel by means of a bicycle.

You will see per in many similar examples:

Mi skribas per krajono = I write with a pencil
Mi sendis ĝin per retpoŝto = I sent it by email

Because biciklo here is just naming the means of transport in a general way: by bicycle.

Per biciklo means using a bicycle in general.
If you said per la biciklo, that would usually mean using the bicycle — a specific bicycle already known from context.

So:

per biciklo = by bicycle
per la biciklo = by/using the bicycle

Yes. Those are possible alternatives.

• Mi veturas per biciklo al la biblioteko = I travel to the library by bicycle
• Mi iras bicikle al la biblioteko = I go to the library by bicycle
• Mi biciklas al la biblioteko = I cycle to the library

The version with per biciklo is very clear and beginner-friendly.
Biciklas focuses more directly on the action to cycle.

Because al already marks direction toward a place.

In Esperanto, you normally do not add -n after al:

al la biblioteko = to the library

The accusative -n can also show direction in some situations, but not after al, because al already does that job.

So:

Mi iras al la biblioteko = correct
Mi iras al la bibliotekon = not standard

La is the definite article, meaning the.

Esperanto has no separate word for a/an. So:

la biblioteko = the library
biblioteko = a library or just library, depending on context

In this sentence, la biblioteko suggests a specific library that the speaker has in mind.

The ending -as marks the present tense.

So veturas can mean things like:

• I am traveling
• I travel
• I am going
• I ride

The exact English translation depends on context. Esperanto tense is simpler than English, so one form can cover several English present-time meanings.

Yes. Esperanto word order is fairly flexible because prepositions and endings already show the relationships between words.

The sentence as given is a neutral, natural order:

Mi veturas per biciklo al la biblioteko.

But you could also say:

Al la biblioteko mi veturas per biciklo.
This emphasizes the destination.

Per biciklo mi veturas al la biblioteko.
This emphasizes the means of transport.

The original order is the most straightforward for learners.