  We show that the last zero before time $t$ of a recurrent Bessel process with
drift starting at $0$ has the same distribution as the product of an
independent right censored exponential random variable and a beta random
variable. This extends a recent result of Schulte-Geers and Stadje (2017) from
Brownian motion with drift to recurrent Bessel processes with drift. Our proof
is intuitive and direct while avoiding heavy computations. For this we develop
a novel additive decomposition for the square of a Bessel process with drift
that may be of independent interest.
