Aims: We aim at detecting H\(_2\)O in the atmosphere of the hot Jupiter HD 209458 b and perform a multi-band study in the near infrared with CARMENES. Methods: The H\(_2\)O absorption lines from the planet's atmosphere are Doppler-shifted due to the large change in its radial velocity during transit. This shift is of the order of tens of km s\(^{-1}\), whilst the Earth's telluric and the stellar lines can be considered quasi-static. We took advantage of this to remove the telluric and stellar lines using SYSREM, a principal component analysis algorithm. The residual spectra contain the signal from thousands of planetary molecular lines well below the noise level. We retrieve this information by cross-correlating the spectra with models of the atmospheric absorption. Results: We find evidence of H\(_2\)O in HD 209458 b with a signal-to-noise ratio (S/N) of 6.4. The signal is blueshifted by --5.2 \(^{+2.6}_{-1.3}\) km s\(^{-1}\), which, despite the error bars, is a firm indication of day-to-night winds at the terminator of this hot Jupiter. Additionally, we performed a multi-band study for the detection of H\(_2\)O individually from the three NIR bands covered by CARMENES. We detect H\(_2\)O from its 1.0 \(\mu\)m band with a S/N of 5.8, and also find hints from the 1.15 \(\mu\)m band, with a low S/N of 2.8. No clear planetary signal is found from the 1.4 \(\mu\)m band. Conclusions: Our significant signal from the 1.0 \(\mu\)m band in HD 209458 b represents the first detection of H\(_2\)O from this band, the bluest one to date. The unfavorable observational conditions might be the reason for the inconclusive detection from the stronger 1.15 and 1.4 \(\mu\)m bands. H\(_2\)O is detected from the 1.0 \(\mu\)m band in HD 209458 b, but hardly in HD 189733 b, which supports a stronger aerosol extinction in the latter.