We study a dilute gas of attractive bosons confined in a harmonic cylinder, i.e., under cylindric confinement due to a transverse harmonic potential. We introduce a many-body wavefunction which extends the Bethe ansatz proposed by McGuire (1964 J. Math. Phys. 5 622) by including a variational transverse Gaussian shape. We investigate the ground-state properties of the system comparing them with those of the one-dimensional (1D) attractive Bose gas. We find that the gas becomes ultra 1D as a consequence of the attractive interaction: the transverse width of the Bose gas reduces by increasing the number of particles up to a critical width below which there is the collapse of the cloud. In addition, we derive a simple analytical expression for the symmetry-breaking solitonic density profile of the ground state, which generalizes the one deduced by Calogero and Degasperis (Calogero F and Degasperis A 1975 Phys. Rev. A 11 265). This bright-soliton analytical solution shows near the collapse small deviations with respect to the three-dimensional (3D) mean-field numerical solution. Finally, we show that our variational Gauss–McGuire theory is always more accurate than the McGuire theory. In addition, we prove that, for small numbers of particles, the Gauss–McGuire theory is more reliable than the mean-field theory described by the 3D Gross–Pitaevskii equation.