Calculating ΔH from bomb calorimetry
To quote Sime's textbook on Physical Chemistry, experiment 3 on the measurement of heats of combustion of hydrocarbons using bomb calorimetry: &quot;we will assume that $\Delta U = \Delta U_r^o$; that is, we will assume that $\Delta U$ is independent of pressure&quot;. There is no further justification of the statement. The Parr Instrument Company provides an introductory guide to bomb calorimetry (document 483M) which has the following to say:

Users interested in high precision calorimetry
will understand that test results obtained in a bomb
calorimeter express calorific values obtained at constant
volume. This differs from the usual conditions
under which fuels are burned at constant pressure
rather than constant volume. If the sample contains
elements which normally would increase in volume
after combustion, a correction must be applied to
account for the heat equivalent of this work. This
value is so small as to be negligible in routine work,
and it usually is disregarded.

The required pressure correction can be computed from thermal expansion and isothermal compressibility coefficients. For instance, for water one estimates that if the bomb pressure rises by $\pu{2 GPa}$ over standard pressure then the energy will increase by $\approx \pu{80 J/mol}$. Compare this correction with the heat of combustion of benzoic acid ($\approx \pu{3221 kJ/mol}$) and (assuming the coefficients for benzoic acid are of the same order of magnitude) it's clear that for condensed substances the correction is (often) negligible.
For gases, based on the assumption of ideal gas behavior, an isothermal PV change for the products will leave $\Delta U$ unchanged, so that in fact $\Delta U_r = \Delta U_r^o$.