Learn Hardcore Malay: Bos memberi saya bonus hari ini.

Memberi is the active transitive verb “to give.” The root is beri (“give”), and Malay uses the mem- prefix (one of the meN- prefixes) to turn it into a transitive verb. When mem- attaches to a root beginning with b, the b stays and you get mem- + beri → memberi.

Why is saya placed directly after memberi, with bonus following it, and why don’t I need kepada before saya?

With many meN- verbs (including memberi), the grammar allows two objects in the order: recipient first, then thing given. Here, saya is the recipient (indirect object) and bonus is the thing given (direct object). Because the position marks the recipient, no preposition (kepada) is needed. If you prefer using kepada, you swap to Verb + Direct Object + Prepositional Phrase:
Bos memberi bonus kepada saya.

Why is there no article like a or the before bonus?

Malay does not use articles (a, an, the) the way English does. Nouns appear on their own. If you need to specify “one” you can say satu bonus, but in most contexts you simply say bonus to mean either “a bonus” or “the bonus” depending on context.

Can hari ini (“today”) be placed somewhere else in the sentence?

Yes. Time expressions in Malay are flexible. You can begin with hari ini for emphasis:
Hari ini bos memberi saya bonus.
Or place it at the end:
Bos memberi saya bonus hari ini.
Both are equally correct.

What does bos mean, and is it a Malay word or a loanword?

Bos is a loanword from English boss. It normally refers to your direct supervisor or manager. A more formal Malay term for “employer” (the company owner) is majikan, while bos usually means the person you report to daily.

How would you turn this into the passive voice?

Use the passive prefix di- with the root beri → diberi, and mark the agent with oleh:
Saya diberi bonus hari ini oleh bos.
(You can also drop oleh bos if the agent is obvious.)