You have to first realize that loops and meanders are not a good place to run a pipeline. Look for a place where you can cross with a more perpendicular angleand where the banks are stable.
With a horizontal drilling installation, (a bit of a misnomer in relation to thrust boring), you are installing with a drilling rig that has been backed off from the riverbank for what could be several hundred meters or more, and the drilling angle is much more horizontal than vertical, 20 deg from the horizon or something. When you initially curve down to the center of the river, then start curving the drilling path back upward to the surface on the other side. You thread that hole with a pull line. Then you redrill the pilot hole to your pipe diameter as you pull your pipe through.
The distance back off the bank will usually depend on your target depth at the river centerline and the curvature you can safely get with your pipe diameter.
The Mississippi can reach depths of 180 feet, thus you might have to back off a mile to curve down under somethign like that, but there are probably better places to cross as well.
For such major crossings, you will want to take a pretty good number of test cores to short list crossing points from a number of potential crossing points, study the results and take more borings from those shortlisted, until you can finally decide on the final location. The river is probably navigable, so ask the COE for advice at an early stage. You'll need their permit to do it anyway.
Let your acquaintances be many, but your advisors one in a thousand’ ... Book of Ecclesiasticus