Are there time limits on reading an e-book, or on the number of people reading it?

Yes, there can be various restrictions on e-books depending on the publisher. Please see here for further details:

www.bristol.ac.uk/library/find/ebooks/.

If the 'read online' button is greyed out, it might be that a certain number of users are logged into that book and it has reached its user limit. 

We recommend refreshing the page intermittently and hopefully the 'read online' button will appear clickable soon.