  We numerically study bootstrap percolation on Kleinberg's spatial networks,
in which the probability density function of a node to have a long-range link
at distance $r$ scales as $P(r)\sim r^{\alpha}$. Setting the ratio of the size
of the giant active component to the network size as the order parameter, we
find a critical exponent $\alpha_{c}=-1$, above which a hybrid phase transition
is observed, with both the first-order and second-order critical points being
constant. When $\alpha<\alpha_{c}$, the second-order critical point increases
as the decreasing of $\alpha$, and there is either absent of the first-order
phase transition or with a decreasing first-order critical point as the
decreasing of $\alpha$, depending on other parameters. Our results expand the
current understanding on the spreading of information and the adoption of
behaviors on spatial social networks.
