A low-cost method for carbon nanotubes (CNTs) network production from solutions on flexible polyethylene naphthalate substrates has been adopted to prepare high quality and well characterized SWCNT bundle layers to be used as the active layer in chemiresistor gas sensors. Two types of SWCNTs have been tested: pristine SWCNTs, deposited from a surfactant solution, and covalently functionalized SWCNTs, deposited from a dimethyl-acetamide solution. The humidity effects on the sensitivity of the SWCNTs network to NH3 have been investigated. The results show that relative humidity favors the response to NH3, confirming recent theoretical predictions. The COOH-functionalized sample displays the largest response owing to both its hydrophilic nature, favoring the interaction with H2O molecules, and its largest surface area. Compared to data available in the literature, the present sensors display a remarkable sensitivity well below the ppm range, which makes them quite promising for environmental and medical applications, where NH3 concentrations (mostly of the order of tens of ppb) have to be detected.