Learn Hardcore Italian: Vado all’università in autobus ogni mattina. - I go to the university by bus every morning.

This comes from combining the preposition a with the feminine article before a vowel. Normally a + la = alla, but because università starts with a vowel, la elides to l’. So you get a + l’ = all’, giving all’università.

Why is it in autobus instead of con l’autobus?

In Italian, when talking about your means of transport generally, we use in + vehicle without an article: in macchina, in treno, in autobus. Saying con l’autobus (“with the bus”) isn’t wrong, but in autobus is more idiomatic for describing how you travel.

Why isn’t there an article before autobus in in autobus?

Fixed expressions of transport with in typically drop the article to refer to the mode, not a specific vehicle. You’d say in taxi, in pullman, in autobus, but if you want a particular bus you can say in quell’autobus or con l’autobus numero 5.

Could we use prendo l’autobus instead of vado in autobus?

Yes! Prendo l’autobus means “I take the bus” (focus on boarding the vehicle). Vado in autobus means “I go by bus” (focus on the journey/mode). Both are correct and often interchangeable.

Why is it ogni mattina and not tutte le mattine or just la mattina?

Ogni mattina uses ogni + singular noun to mean “every morning.”
Tutte le mattine (“all the mornings”) is also possible and has the same meaning, though a bit longer.
La mattina by itself usually means “in the morning” in a general sense, not necessarily “each” morning.

What is the gender and plural form of università?

Nouns ending in -tà are always feminine, so università is feminine singular. Its plural is invariable: le università. Note the stress falls on the final -à.

Can ogni mattina be placed at the beginning of the sentence?

Absolutely. Italian word order is flexible for adverbs and time expressions.
You can say:
Ogni mattina vado all’università in autobus.
This fronting simply adds emphasis on when you go.