Learn Hardcore Esperanto: Ŝi havas bonan ideon: veturi per biciklo al la oficejo anstataŭ iri per aŭtobuso. - She has a good idea: to go by bicycle to the office instead of going by bus.

iri = to go, to walk, general movement from one place to another. Often neutral, but strongly associated with going on foot.
veturi = to travel / to ride / to drive using a vehicle (something that moves and carries you).

So:

veturi per biciklo focuses on travelling by means of a vehicle (the bicycle).
iri per aŭtobuso is also correct: you can use iri with per
- vehicle. The writer simply varies the verbs for style; both could be veturi or both iri without changing the basic meaning much.

Why does it say bonan ideon and not bona ideo?

Because bonan ideon is the direct object of havas.

Ŝi havas kion? → bonan ideon.
Direct objects take -n in Esperanto: ideo → ideon.

So bonan ideon is the accusative form, showing that it is what she has.

Why does bona also become bonan?

Adjectives in Esperanto agree with the noun they describe in:

number (singular/plural: bona ideo, bonaj ideoj)
case (nominative/accusative: bona ideo, bonan ideon)

Since the noun is ideon (accusative singular), the adjective must match:

bona ideo (a good idea – subject)
bonan ideon (a good idea – object)

So the -n is added to both the noun and its adjective.

What does per mean in per biciklo and per aŭtobuso?

per means by means of / using.

veturi per biciklo = to travel by bicycle, using a bicycle.
iri per aŭtobuso = to go by bus, using a bus.

So per + noun is the normal way to say by X in the sense of using a tool, instrument, or means of transport.

Can I say bicikle or aŭtobuse instead of per biciklo / per aŭtobuso?

Yes, very often you can:

veturi bicikle al la oficejo
iri aŭtobuse al la oficejo

The adverbs bicikle and aŭtobuse are common and natural. In practice:

per biciklo ≈ bicikle
per aŭtobuso ≈ aŭtobuse

Both styles are widely understood. Using per is slightly more explicit as “by means of…”, while the -e forms are a bit more compact.

Why is it al la oficejo, not just al oficejo?

la is the definite article, like English the.

al oficejo = to an office (some unspecific office)
al la oficejo = to the office (a specific, known office – here, her workplace)

In this sentence we clearly mean her usual office, so la is natural.

Could it be al la oficejon with -n?

You will mostly see one of these:

al la oficejo
(al) oficejen

In everyday Esperanto:

You normally do not add -n when you already have al.
Direction can be shown either with al or with the accusative -n, not both together, except in some special or emphatic styles.

So for a learner, prefer:

al la oficejo (most straightforward here), or
oficejen if you want to use the bare accusative of direction.

Is veturi here an infinitive, like English to travel?

Functionally, yes.

Esperanto does not have a special infinitive form; the dictionary form in -i (veturi, iri, manĝi etc.) is used both as:

the “infinitive” (to travel, to go, to eat), and
the base form for conjugation (from which veturas, iris, etc. are built).

In this sentence, veturi and iri act like English infinitives:

bonan ideon: veturi… anstataŭ iri…
→ a good idea: to travel… instead of going…

How does anstataŭ work with verbs like veturi and iri?

anstataŭ means instead of and it links parallel things:

nouns: kafo anstataŭ teo (coffee instead of tea)
verbs: legu anstataŭ spekti (read instead of watching)

With verbs, you just use the same -i form:

veturi per biciklo … anstataŭ iri per aŭtobuso
→ two verb phrases: veturi per biciklo and iri per aŭtobuso.

The subject ŝi is understood to apply to both verbs; you do not repeat it.

Can I drop iri and say only anstataŭ per aŭtobuso?

That would sound incomplete or at least very elliptical.

anstataŭ iri per aŭtobuso clearly says instead of going by bus.
anstataŭ per aŭtobuso is only instead of by bus, with the verb missing.

Native-style Esperanto normally keeps the verb after anstataŭ when you are contrasting actions, so you should keep iri here.

Why is there a colon after ideon? Could I leave it out?

The colon introduces the explanation of what the bona ideo actually is, just like in English:

She has a good idea: to travel by bike…

You could also write:

Ŝi havas bonan ideon veturi per biciklo… (without a colon), or
Ŝi havas bonan ideon, nome veturi per biciklo… (namely to travel by bike…)

So the colon is not grammatically required, but it is good style to clearly mark that the second part explains the idea.

How free is the word order? Could I say veturi al la oficejo per biciklo?

Yes, Esperanto word order is quite flexible, especially for complements like per biciklo and al la oficejo.

All of these are grammatical:

veturi per biciklo al la oficejo
veturi al la oficejo per biciklo
al la oficejo veturi per biciklo (more marked emphasis / poetic)

The neutral, most typical order is what you see in the sentence: verb first, then its complements in a natural flow. Moving phrases around is mainly a matter of emphasis and style, not correctness.

Could I say veturi bicikle oficejen instead of veturi per biciklo al la oficejo?

Yes, that is a compact alternative:

bicikle instead of per biciklo
oficejen (accusative of direction) instead of al la oficejo

So:

veturi bicikle oficejen ≈ veturi per biciklo al la oficejo

Both versions are understandable and correct. The original sentence simply uses the more explicit per and al la forms, which are very clear for learners.