Here is a picture of Hall’s Circulating Library in Margate( try as I could I couldn’t find a picture of one from 18th Century Bath-sorry). However...this will give you some idea of the type of places they were :

These places were private lending libraries, if you like, where you could subscribe, and pay to borrow the latest books.

Tobias Smollet in another novel set partly in Bath ,and one of the books Lydia likes to readThe Expedition of Humphrey Clinkerdescribes a circulating library as the place:

…where we read novels, plays pamphlets, and news-papers for so small a subscription as a crown(5 shillings-JW) a quarter

This is the type of place Lydia has sent Lucy to in order to get the latest novels, with various degrees of success.

In fact the places to which she sent her servant Lucy to actually existed in Bath.

Mr Lewis Bull( line 8 scene ii )was a book seller in Bath, who also ran a circulating library. His shop( which also sold knick-knacks etc ) was opposite Gydes rooms on the Lower walks.( which have already been mentioned by Fag in Scene i)