Using first-principles calculations, we show that p-doped blue phosphorene can be obtained by molecular doping with 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4-TCNQ) and 1,3,4,5,7,8-hexafluorotetracyanonaphthoquinodimethane (F6-TNAP), whereas n-doped blue phosphorene can be realized by doping with tetrathiafulvalene (TTF) and cyclooctadecanonaene (CCO). Moreover, the doping gap can be effectively modulated in each case by applying an external perpendicular electric field. The optical absorption of blue phosphorene can be considerably enhanced in a broad spectral range through the adsorption of CCO, F4-TCNQ, and F6-TNAP molecules, suggesting potential of the doped materials in the field of renewable energy.