Bessel beams are invariant solutions to the Helmoltz equation that can also propagate, with finite pulse energy at high intensity, in a quasi-invariant regime in transparent dielectrics. Homogeneous energy is deposited along a line focus by infrared ultrashort pulses. If the cone angle is sufficiently high, the laser-deposited energy density is enough to open nanochannels in glasses or sapphire with a single laser pulse. This has found applications in the field of glass cutting via the technique of "stealth dicing". Here we address two important challenges in this field. First, high quality Bessel beams are essential for controlled energy deposition. Second, the maximal angle used up to here for channel drilling was 26° for 800 nm laser central wavelength. This enabled the formation of channels with diameters down to typically 300 nm in glass and sapphire. It is questionable if higher cone angles could also produce channels with potentially smaller diameters. Here, we generate high quality Bessel-Gauss beams with a setup based on reflective, off-axis axicons. The Bessel zone exceeds 100 µm for cone angles up to 35 degrees. This corresponds to central spot diameter down to 0.5 µm FWHM. We qualified these beams with a 100 fs laser source centered at 800 nm wavelength. We report nanochannel drilling down to typically 100 nm over at least 30 µm length in glass. Our approach opens novel perspectives for high quality Bessel beam generation but also for the highly confined laser-matter interaction for high precision processing of transparent dielectrics.