  It was recently shown (by the second author and D\'{i}az Garc\'{i}a, Krutov,
Somberg, and Strung) that every relative line module over an irreducible
quantum flag manifold $\mathcal{O}_q(G/L_S)$ admits a unique
$\mathcal{O}_q(G)$-covariant connection with respect to the Heckenberger-Kolb
differential calculus $\Omega^1_q(G/L_S)$. In this paper we show that these
connections are bimodule connections with an invertible associated bimodule
map. This is proved by applying general results of Beggs and Majid, on
principal connections for quantum principal bundles, to the quantum principal
bundle presentation of the Heckenberger-Kolb calculi recently constructed by
the authors and D\'{i}az Garc\'{i}a. Explicit presentations of the associated
bimodule maps are given first in terms of generalised quantum determinants,
then in terms of the FRT presentation of the algebra $\mathcal{O}_q(G)$, and
finally in terms of Takeuchi's categorical equivalence for relative Hopf
modules.
