Learn Hardcore Japanese: watasi ha zyuuzi ni basu ni norimasu.

は is the topic marker. It tells the listener that we’re talking about “me” (私) as the topic of the sentence. In English it often corresponds to “as for” or just sets the subject: “As for me, …”

Why are there two に particles in 十時にバスに乗ります?

Japanese uses に for different purposes:

十時に marks the point in time (at ten o’clock).
バスに乗ります uses に to indicate the means or vehicle you board (“get on the bus”).

Why don’t we use を with 乗ります (i.e. why not バスを乗ります)?

Some verbs use に instead of を to show what you enter or board. 乗る/乗ります (“to ride, to get on”) always takes に for the vehicle or transportation mode.

Where should time expressions like 十時に be placed in a sentence?

Time expressions typically come before the verb, often right after the topic. You can say:

私は十時にバスに乗ります or
十時に私はバスに乗ります
Both are grammatical; the first is more common because the natural flow is Topic → Time → Other elements → Verb.

What is the difference between 乗ります and its plain form?

乗ります is the polite (ます-form) of 乗る.

Polite present/future: 乗ります (“will ride/get on”)
Plain/dictionary: 乗る (“[I] ride” or a general statement)

How do you change 乗ります to past or negative forms?

In polite speech:

Past: 乗りました (“I got on/rode”)
Negative: 乗りません (“I do not get on”)
Past negative: 乗りませんでした (“I did not get on”)

Can you omit 私は and just say 十時にバスに乗ります?

Yes. If the topic is clear from context, you can drop 私は. Japanese often omits pronouns when they’re understood.

Is 乗ります an irregular verb?

No, 乗る is a regular u-verb (also called a Godan verb). Its stem is 乗り-, to which you add ます, ました, ません, etc.

Can this structure be used with other vehicles or things you enter?

Absolutely. Just replace バス with the vehicle or mode of transport, always keeping に:

十時に電車に乗ります (“I’ll get on the train at 10.”)
エレベーターに乗ります (“I ride the elevator.”)
馬に乗ります (“I ride a horse.”)