In this Letter, we present an all-fiber bismuth (Bi)-doped germanosilicate fiber laser that is continuously tunable within the range of 1425–1475 nm, enabled by a tunable optical filter. A maximum output power of 86.4 mW was achieved at 1450 nm with a slope efficiency of 13.7%. It is, to the best of our knowledge, the first demonstration of an all-fiber tunable continuous-wave (CW) bismuth-doped fiber laser (BDFL) operating in the E + S band. Moreover, a bismuth-doped fiber amplifier (BDFA) was constructed to further scale the laser output power to 159.2 mW with a 21% slope efficiency. Across the 1425–1475 nm range, we achieved >117 mW output power with >50 dB in-band optical signal-to-noise ratio (OSNR).