In aerodynamics, what methods do people use to calculate the geometry of a wing (and body) needed to obtain a bell shaped lift distribution? Please go into as much detail as possible for a stack exchange answer. Also, when feasible, please provide resources to back up claims.
For an unswept wing of an at least moderate aspect ratio in subsonic flow you can use the Multhopp panel tabulation. This divides the wing into an odd number of sections and is easily implemented on a computer.
The way to achieve a bell distribution is to start with an arbitrary wing design and then to iterate chord and twist in order to achieve the desired distribution for the desired angle of attack.
I think you are referring to a bell-shaped lift distribution for the entire aircraft.
If you take a look at the SU-27 fight jet, you can see that the wings aren't distinct from the center body of the jet. You see that wings merge together with the central body, creating one single lift body of the aircraft, as opposed to the traditional design where wings and the center of the aircraft.
This design has been proven to be extremely aerodynamic, and this aerodynamic configuration is still being used today on many fighter jets, examples include the Chinese J-11 and the Russian SU-35, which are all very good jets.
Moreover, if you are looking to reduce drag overall, you can also try to have winglets for your aircraft. They can reduce the amount of vortex drag created by your wings. But just be careful because winglets will reduce the maneuverability of your aircraft and will negatively impact supersonic flight performance.
Hopefully this is the answer you were looking for. If not, have a nice day :)