The dissolution of a gas bubble in a confined geometry is a problem of interest in technological applications such as microfluidics or carbon sequestration, as well as in many natural flows of interest in geophysics. While the dissolution of spherical or sessile bubbles has received considerable attention in the literature, the case of a two-dimensional bubble in a Hele-Shaw cell, which constitutes perhaps the simplest possible confined configuration, has been comparatively less studied. Here, we use planar laser-induced fluorescence to experimentally investigate the diffusion-driven transport of dissolved CO2 that propagates from a cylindrical mm-sized bubble in air-saturated water confined in a horizontal Hele-Shawcell. We observe that the radial trajectory of an isoconcentration front, r(f) (t), evolves in time as approximately r(f) - R-0 alpha root t, where R-0 denotes the initial bubble radius. We then characterize the unsteady CO2 concentration field via two simple analytical models, which are then validated against a numerical simulation. The first model treats the bubble as an instantaneous line source of CO2, whereas the second assumes a constant interfacial concentration. Finally, we provide an analogous Epstein-Plesset equation with the intent of predicting the dissolution rate of a cylindrical bubble.