This annual event across the country takes place from Wednesday to Saturday 1 to 4 January 2020. Many of the 3-hour searches for plants in flower take place informally or on an individual basis. At the time of writing I am only aware of one formal meeting nearby, but it is outside the Bristol region. The Somerset Rare Plants Group will be meeting in Taunton at 11 am on Saturday 4 January. Details are available on their website.
BSBI New Year Plant Hunt