Note that although the spacetime fibre bundle

is unique, as is the electromagnetic potential

(or alternatively the Maxwell tensor

),
the bundle connection
is different for each particle, as it depends on the particle's charge,
e.
(Alternatively we could instead regard each particle or particle-type as defining a completely
different set of U(1) fibres over the same base Minkowski space

, with a specific bundle connection then being unique to each such fibre set)...
This is in contrast to the metric (Riemannian) connection of ยง14.7, which can be regarded as an intrinsic property of spacetime, and doesn't vary depending on what you are applying it to!