The answer to this question could vary depending on exactly which time you are asking about in reference to Beatrice helping Roy. I would say that the first time that Beatrice offers to help Roy occurs in chapter 7. Roy is attempting to bring Mullet Fingers a shoe box that contains . . . shoes. Beatrice stops him and doesn't actually believe that the box contains shoes. She is surprised to find out that the box actually does, but she is still very much suspicious of Roy.
"Why are you carryin' around an extra pair of sneakers?"
Roy doesn't actually have a reason that he can verbalize, but I think that Beatrice can sense that he has good intentions; however, she isn't about to let Roy deliver the shoes. Beatrice offers to help Roy out. She offers to take the shoes to the barefoot running kid (Mullet Fingers) if Roy promises to stop investigating the kid.
"I'll make you a little deal."
"Go on," said Roy.
"I'll see that the barefoot kid gets these shoes, but only if you promise to leave him alone. No more spying."
"So you do know him!"
Basically, Beatrice offers to help Roy out the first time as a bribe to keep him away from her brother.