As well as some special guests, and picturesque locations, we're giving you the chance to enter our daily competition.
You can find today's question further down this page, but you'll have to be quick as the phone lines close at midday.
Jane Austen's Bath: how the city inspired one of Britain's finest novelists
Highlights
If you want to see so some of the week's highlights, click on the links at the top of the page.
Competition
Today's competition has now closed. The winner is Roy Powell from Melksham, West Wiltshire.
But don't worry, there will be another chance to enter tomorrow.
Yesterday's winner was Jacky Bonner from Salisbury, Wiltshire.
Tomorrow
We take a look at the healing powers of the spa waters and how the Georgian period which saw the construction of the Royal Mineral Water Hospital.
Friday
On our last day of specially extended programmes, we look at Bath's popularity as a film location and the house where parts of Vanity Fair were filmed.
And we'll be concluding our week in Bath by asking whether the town, along with others could make Britain the spa capital of the world.
Breakfast in Bath, BBC One until Friday 18 July, 0830 to 0915 BST
Competition rules
1. The competition is open to all residents of the British Isles, including the Channel Islands, aged 18 years or over except BBC employees, their close relatives and anyone connected with the competition.
2. Entry to the competition is by calling telephone number 08700 109 771. Callers will be asked to answer 1 question.
3. All entrants must supply their names and addresses and daytime telephone number.
4. The winning entrant will be the first correct entry drawn after the closing date.
5. The prize changes each day.
6. The prize is as stated. There is no cash alternative.
7. The BBC's decision as to the winner is final. No correspondence relating to the competition will be entered into.
8. The winner will be notified within 2 days of the closing date by post (or telephone).
9. Only one entry is allowed per entrant or There is no limit on the number of entries per entrant.
10. Entrants must agree to take part in any post-competition publicity.