Learn Hardcore Indonesian: Selama menunggu bus, kauperiksa jadwal di aplikasi. - While waiting for the bus, you check the schedule in the app.

selama = during/for the duration of. It highlights the whole span of time. Your sentence suggests “during the time you were waiting.”
sambil = while (two actions done simultaneously by the same subject). Very natural here: Sambil menunggu bus, kau periksa jadwal di aplikasi.
sementara = while/whereas; common in writing and neutral: Sementara menunggu bus, ...
ketika/saat = when (point or occasion). Also fine, slightly more event-like than durational: Ketika/Saat menunggu bus, ...
selagi = while/as long as; informal-ish: Selagi menunggu bus, ...

Who is doing the waiting in Selama menunggu bus? Do I need to say the subject explicitly?

By default, the subject is understood to be the same as the main clause (“you”). If it’s different, state it:

Selama ayah menunggu bus, kau periksa jadwal di aplikasi. (While Dad was waiting, you checked…)

Why is kauperiksa written as one word? Can I write kau periksa instead?

Indonesian allows the proclitic pronoun kau- to attach to the verb it governs, so kauperiksa is correct. You will also see the separated form kau periksa in modern writing. Both are widely understood; the attached form looks a bit more literary. (Similarly, first-person ku- attaches: kuperiksa.)

Is kau the same as kamu or Anda? What’s the register?

kau (short for engkau) = intimate/poetic/literary; normal in some regions (e.g., parts of Sumatra), but in big-city speech it can sound literary or brusque to strangers.
kamu = everyday neutral “you.”
Anda = polite/formal “you.” Choose based on relationship and formality.

Why is the base verb periksa used instead of memeriksa?

With kau (and also with the clitic ku-), Indonesian often uses the bare verb: kau periksa/kuperiksa. You can also say Kau memeriksa jadwal…, which is fully grammatical.

With kamu, the statement form normally takes meN-: Kamu memeriksa…; Kamu periksa… tends to sound like a command.
With third person, use meN-: Dia memeriksa… (not usually Dia periksa… in a neutral statement).

Does kauperiksa mean past tense (“you checked”)?

Indonesian verbs don’t mark tense. Time is inferred from context or time words:

Past: tadi/kemarin/sudah/telah — Selama menunggu bus tadi, kau sudah memeriksa jadwal di aplikasi.
Progressive: sedang — Kau sedang memeriksa jadwal…
Future: akan/nanti — Nanti kau memeriksa jadwal…

Is bus the correct spelling? I’ve seen bis too.

The current standard spelling is bus. The older bis still appears in informal usage, but dictionaries and official writing prefer bus.

Is di aplikasi idiomatic? When would I use pada, di dalam, or melalui?

di aplikasi (“in the app”) is very common in everyday Indonesian. Alternatives:

pada aplikasi — more formal (“on the application”).
di dalam aplikasi — stresses “inside/within the app” (slightly more literal).
melalui aplikasi — “through/via the app,” emphasizing the means.

Does jadwal need an article like “the/a”? How do I say “the bus schedule”?

Indonesian has no articles. jadwal is neutral and can be specific or general from context. To make it clearly specific:

jadwalnya (“the schedule”/“its schedule”)
jadwal itu (“that schedule/the schedule”)
jadwal bus (“the bus schedule”) Example: Selama menunggu bus, kauperiksa jadwal bus di aplikasi.

Why is there a comma after the opening phrase?

A comma separates an initial adverbial phrase/clause from the main clause. Selama menunggu bus, is an introductory time phrase, so a comma is standard.

What would a more casual version sound like?

Very natural colloquial options include:

Sambil nunggu bus, kamu ngecek jadwal di aplikasi.
Pas nunggu bus, kamu ngecek jadwal di aplikasi. Here nunggu = informal for menunggu, and ngecek/mengecek = informal/formal for memeriksa/cek.

How would I change the voice or emphasis?

Passive: Jadwalnya diperiksa (olehmu) di aplikasi. (agent optional)
Object fronting (common in speech): Jadwalnya kamu periksa di aplikasi.
First person: Selama menunggu bus, kuperiksa jadwal di aplikasi. / Selama menunggu bus, aku memeriksa jadwal di aplikasi.