What are two things Bud feels he cannot live without?

In my opinion, Bud would probably say that he couldn't live without more than only two things. The suitcase that Bud brings with him everywhere carries all of the "treasures" that he holds most dear to him, so anything from that suitcase would work for this list. Readers are told on two different occasions that Bud would not go anywhere without the suitcase itself. The first time is when Mrs. Amos takes the suitcase in order to control Bud:

This shall be our assurance that nothing comes up missing from the house and that this little animal is still here in the morning. He is far too attached to those treasures to go anywhere without them.

The second person to comment on Bud's attachment to the suitcase is Lefty Lewis:

He said, "I’ll tell you what, Bud, you don't go anywhere without this, do you?"
I said, "No, sir."

Bud has a variety of important things in the suitcase. The first is a blanket, and Bud is very particular about how that blanket gets folded and placed into the suitcase. Bud also has a bag of rocks/stones in the suitcase, and those stones become pivotal for Bud proving his identity to Calloway later in the book. Bud also has a picture of his mother in the suitcase.