The Large Magellanic Cloud (LMC) is a Milky Way (MW) satellite that is massive enough to gravitationally attract the MW disc and inner halo, causing significant motion of the inner MW with respect to the outer halo. In this work, we probe this interaction by constructing a sample of 9866 blue horizontal branch (BHB) stars with radial velocities from the DESI spectroscopic survey out to 120 kpc from the Galactic centre. This is the largest spectroscopic set of BHB stars in the literature to date, and it contains four times more stars with Galactocentric distances beyond 50 kpc than previous BHB catalogues. Using the DESI BHB sample combined with SDSS BHBs, we measure the bulk radial velocity of stars in the outer halo and observe that the velocity in the Southern Galactic hemisphere is different by 3.7$\sigma$ from the North. Modelling the projected velocity field shows that its dipole component is directed at a point 22 deg away from the LMC along its orbit, which we interpret as the travel direction of the inner MW. The velocity field includes a monopole term that is $-24$ km s$^{-1}$, which we refer to as compression velocity. This velocity is significantly larger than predicted by the current models of the MW and LMC interaction. This work uses DESI data from its first 2 yr of observations, but we expect that with upcoming DESI data releases, the sample of BHB stars will increase and our ability to measure the MW–LMC interaction will improve significantly.