We present the first sub-mJy (≈0.7 mJy beam-1) survey to be completed below 100 MHz, which is over an order of magnitude deeper than previously achieved for widefield imaging of any field at these low frequencies. The high-resolution (15×15 arcsec) image of the Boötes field at 34-75 MHz is made from 56 hours of observation with the LOw Frequency ARray (LOFAR) Low Band Antenna (LBA) system. The observations and data reduction, including direction-dependent calibration, are described here. We present a radio source catalogue containing 1948 sources detected over an area of 23.6 deg2, with a peak flux density threshold of 5σ. Using existing datasets, we characterise the astrometric and flux density uncertainties, finding a positional uncertainty of ∼ 1.2 arcsec and a flux density scale uncertainty of about 5 per cent. Using the available deep 144-MHz data, we identified 144-MHz counterparts to all the 54-MHz sources, and produced a matched catalogue within the deep optical coverage area containing 829 sources. We calculate the Euclidean-normalised differential source counts and investigate the low-frequency radio source spectral indices between 54 and 144 MHz. Both show a general flattening in the radio spectral indices for lower flux density sources, from ∼-0.75 at 144-MHz flux densities between 100 and 1000 mJy to ∼-0.5 at 144-MHz flux densities between 5 and 10 mJy. Such flattening is attributable to a growing population of star forming galaxies and compact core-dominated AGN.