Chapter five is your best bet for sentences that are about Bud's mom.  It is also the best chapter to find quotes that are spoken by Bud's mom.  Bud's mom is dead, so chapter five is mainly a flashback.  

One of my favorite lines from Bud's mother is the following:

She'd tell me, "Especially don't you ever let anyone call you Buddy. I may have some problems, but being stupid isn't one of them.  I would've added that dy onto the end of your name if I intended for it to be there. I knew what I was doing. Buddy is a dog's name, or a name that someone's going to use on you if they're being false-friendly. Your name is Bud, period."

I like the quote a lot because people are always shortening my name, which really bothers me.  My own mother actually uses the same argument that Bud's mom uses.  The line shows that Bud's mother was very intentional about her actions and choices.  She further explains why she chose "Bud" and not "Buddy."  

"A bud is a flower-to-be. A flower-in-waiting. Waiting for just the right warmth and care to open up. It's a little fist of love waiting to unfold and be seen by the world. And that's you."

Chapter five also contains a line from Bud's mother that is symbolic throughout the entire book. 

"And Bud, I want you always to remember, no matter how bad things look to you, no matter how dark the night, when one door closes, don't worry, because another door opens."

At that point in Bud's life, he thought that she was talking about an actual door.  But during the rest of the story, Bud realizes that his mother was talking about metaphorical doors.  The doors that she was talking about were opportunity doors.  For example, when the Amos family was going to send Bud back to the orphanage, it gave him the opportunity to begin searching for his father.