We first visited during its opening few weeks in October 2012, before it had been awarded its Michelin star (in 2014). We were lucky enough that James Knappett was head chef that day. Our set menu (see picture) consisted of 13 courses. Don't worry they are quit small, but rich enough and full of flavour to fill you by the end. The set menu is the only option on offer, but they were kind enough to substitute some of the dishes on the night for me (at the time I was not that keen on mussels).
I understand that they get booked up very quickly, and so would recommend making a reservation well in advance. A good option maybe to visit Bubbledogs first and ask to have a sneak peak. Be prepared for some unusual dishes and to try things you have never had before - including duck hearts which were particularly tasty.
Of course, they have a good selection of wine, champagne and cocktails to tantalize the taste buds.