Why does Crispin fear that he and Bear have been trapped?

It looks like you're referring to Bear's capture in chapter 46. Crispin fears that he and Bear have been trapped because Aycliffe's soldiers have captured Bear, and Crispin does not know how he can rescue his mentor. Furthermore, if Crispin does try to rescue Bear, he may also end up in captivity. Basically, Crispin feels trapped because his nemesis has captured Bear, and it is only a matter of time before they find him as well.
In chapter 47, Crispin tries to figure out where Aycliffe's soldiers have taken Bear. He takes a risk and asks strangers about soldiers dragging a "large red-bearded man" along. He has a bit of luck when some bystanders point him towards the square. So, Crispin makes his way there. He is just in time to see the soldiers drag Bear into a large building. After making inquiries, Crispin discovers that Bear has been taken to Lord Furnival's palace.
It suddenly dawns on Crispin that Aycliffe has taken Bear for a reason: they want him to reveal where Crispin is hiding. Unable to do anything more, Crispin returns to the Green Man Inn.
In chapter 48, Crispin hears a loud commotion from his room. Upon investigating, he finds the tavern room ransacked and the Widow Daventry nursing wounds. It's clear to Crispin that the soldiers came to the inn to look for him during his absence. By the widow's condition, Crispin can see that Aycliffe and his men will stop at nothing to kill him and Bear.
So, from the story, we can see how Crispin may have felt trapped. Bear has been taken, and there is a concerted effort by Aycliffe and Furnival to capture him as well.

The wicked John Aycliffe has discovered Crispin kneeling at prayer in the city cathedral of Great Wexly. Crispin takes off, with Aycliffe's men in hot pursuit. He wants to find Bear to warn him about the danger, but he's nowhere to be seen. Wherever Crispin goes, he seems to be trapped by Aycliffe's men. Somehow he manages to escape, though he loses Bear's dagger in the process.
What's even worse for Crispin is that the city's layout is so confusing; everything looks the same. Even if he can shake off Aycliffe and his men, there still doesn't seem to be any way out. Crispin figures that his best chance is to locate the city walls and from there find the main gate. It sounds like a good idea, but unfortunately when Crispin finally reaches the gate, he finds that it's closed. There's a curfew in force; so no one is allowed in or out of the city. No wonder Crispin feels trapped.