The computation of detection probabilities and arrival time distributions within Bohmian mechanics in general needs the explicit knowledge of a relevant sample of trajectories. Here it is shown how for one-dimensional systems and rigid inertial detectors these quantities can be computed without calculating any trajectories. An expression in terms of the wavefunction Ψ and its spatial derivative _xΨ, both restricted to the boundary of the detectorʼs spacetime volume, is derived for the general case, where the probability current at the detectorʼs boundary may vary its sign.