  We prove explicit uniform two-sided bounds for the phase functions of Bessel
functions and of their derivatives. As a consequence, we obtain new enclosures
for the zeros of Bessel functions and their derivatives in terms of inverse
values of some elementary functions. These bounds are valid, with a few
exceptions, for all zeros and all Bessel functions with non-negative indices.
We provide numerical evidence showing that our bounds either improve or closely
match the best previously known ones.
