Learn Dutch: Ik ben een beetje nerveus.

Because it is used after the verb, not directly in front of a noun. When adjectives come after verbs like zijn (to be) to describe the subject, they act as predicative adjectives and keep their basic, uninflected form.

Does een beetje mean "a bit" or "a little"?

It means both! Een beetje is a fixed phrase used to soften an adjective, exactly like saying "a bit" or "a little" in English.

How do I change this sentence to say "I am very nervous"?

You can swap out the degree modifier een beetje for heel or erg, making it Ik ben heel nerveus or Ik ben erg nerveus. If you wanted to say "too nervous," you would use te nerveus.

Can I drop the word een and just say Ik ben beetje nerveus?

You might hear native speakers drop the een in very fast, casual speech, but the grammatically correct phrase is always een beetje. It is best to learn and use the full phrase!