When you pick coordinates from one coordinate system using one spheroid to another using another spheroid, they will not represent the same real world position anymore. The navigating officer should have requested coordinates from a map using WGS 84.
Alternatively a conversion between the two coordinate systems (Bessel 1841 --> WGS 84) could have been done before inputting coordinates into the GPS system.
Shown below is a sailing course laid between the two Greece islands of Paxos and Antipaxos USING THE SAMME COORDINATES, but projected using two different coordinate systems (using the spheroids WGS 84 and Bessel 1841, respectively). Notice that one of them lays a course grounding the vessel onto Antipaxos, even though the coordinates are the same for both lines.
See also this question, raised earlier:
What's the difference between a projection and a datum?
Geographic coordinate systems (lat/long) are based on a spheroidal
(either truly spherical or ellipsoidal) surface that approximates the
surface of the earth. A datum typically defines the surface (ex radius
for a sphere, major axis and minor axis or inverse flattening for an
ellipsoid) and the position of the surface relative to the center of
Additionally thhe navigator might have been following the wrong heading.
The heading should be constant between two points, and follow a geodesic (straigh line on curved surface) [red line on image]. Often, the heading is continually updated as the ship is moving between the two points when using GPS. The ship will then follow a path that is straight on the flat map [blue line on image], but curved on the sphere (and in the real world).
For your investigation you should inquire if the navigator was following the Grid heading or the True heading (with the latter being the correct heading to use).