  We compute section class relative equivariant Gromov-Witten invariants of the
total space of P^2-bundles of the form P(O+L1+L2)-->C where C is a genus g
curve, O is the trivial bundle, and L1 (resp. L2) is an arbitrary line bundle
of degree k1 (resp. k2) over C. We prove a gluing formula for the partition
functions of these invariants. Using this gluing formula together with
localization techniques, we construct three explicit 3x3 matrices G, U1 and U2
with entries in Q((u))(t0,t1,t2), where u is the genus parameter, and t0,t1,t2
are the equivariant parameters. Then we prove that the partition function of
the section class, ordinary equivariant Gromov-Witten invariants of X is given
by trace(G^(g-1).U1^k1.U2^k2). As an application, we establish a formula for
the partition function of the ordinary Gromov-Witten invariants of any
P^2-bundle X over a curve of genus g for any class which is a Calabi-Yau
section class. We prove that this partition function is given by 3^g(2sin
u/2)^(2g-2).
