Bill in this context is a printed list of items on a theatrical programme or advertisement
RELATED IDIOMS :
fill his shoes = fill his boots :
take over his function or duties and fulfil them satisfactorily - informal
the final straw :
a farther difficulty or annoyance typically minor in itself but coming on top of a whole series of difficulties that makes a situation unbearable
The full version of this is the proverb the last straw breaks the camel's back. The modern form is traceable to Charles Dickens in Dombey and Son (1848). But earlier versions are recorded, including a mid 17th century reference to the last feather breaking a horse's back.