  We study the effects of bulk viscosity on pT spectra and elliptic flow in
heavy ion collisions. For this purpose we compute the dissipative correction df
to the single particle distribution functions in leading-log QCD, and in
several simplified models. We consider, in particular, the relaxation time
approximation and a kinetic model for the hadron resonance gas. We implement
these distribution functions in a hydrodynamic simulation of Au + Au collisions
at RHIC. We find significant corrections due to bulk viscosity in hadron pT
spectra and the differential elliptic flow parameter v2(pT). These corrections
are dominated by viscous corrections to the distribution function. We find that
the relation between df and the bulk viscosity is different in the quark gluon
plasma and hadronic phases. Reliable bounds on the bulk viscosity require
accurate calculations of df in a hadronic resonance gas. Based on v2 spectra at
RHIC we conservatively estimate zeta/s <= 0.05 near freeze-out. We also find
that effects of the bulk viscosity on the pT integrated v2 are small.
