On which cell types do antibodies exist as transmembrane proteins?

The answer is B cells. They are involved in humoral immunity of adaptive immunity. They secrete immunoglobulin (antibodies), which are also the receptors on their cell membrane. These receptors are significant in antigen presentation to T - cells. Memory B cells produce a clone of antibodies.

Naïve B cell

Naïve B cell is known to be a B cell that is not exposed to an antigen. Thus, once naïve B cell is exposed to an antigen, it becomes a plasma cell or memory B cell that secretes antibodies specific to the antigen that was original bound.