I just switched from my basic clarinet to a bass that I'm borrowing from my school. Had been inspecting the instrument after the first time I played and found that the neck is really dirty. It has brown-ish and white build-up and I really want to clean it put but don't know how. Help?

On the inside, not the easily accessible outside

I suggest taking the key off & putting the neck in warm, soapy water for a bit, use a soft nylon brush to loosen the gunk then rinse out with clean water. If that does not remove it all try soaking in vinegar for a few minutes, brush out & rinse. A stronger thing would be to use kettle descaler - diluted as the instructions - instead of the vinegar. It shouldn't harm the metal. While you're at it clean the register vent as well.

What Contra448 said is a very good start then, after you have got it clean, once a month wash it out with baking soda in warm water. I am one of three bass clarinetists in my band and we all do that.
Alan

Thanks you two! Will try that! I'm one of two bass players and we have 8 regular clarinets, and my friend who is the other bass had no clue how