that做宾语从句都可以省略
这里不但省略了that,还省略了一个动词不定式to see
I'm glad （to see that） the bell is working again.
很多描述个人情感的形容词（afraid,glad,happy）和表示确信的词（certain,sure)后面可用可不用that.
I'm glad the bell is working again.相当于I'm glad （to see or to hear or others that） the bell is working again.
所以也可以看做是不定式的省略