How would a spacecraft land on a Bishop's Ring? Would it enter the atmosphere like a space shuttle reentry? And what g-forces would the passengers experience?
There are several possible entry trajectories, probably the least momentum change would be to dock on the outer rim of the ring approaching with a tangential trajectory at the same speed of the ring; when reaching tangent point spacecraft would dock (physically connect to ring structure) and passengers would suddenly start feeling "gravity" (centrifugal force)
If you insist to land "in the normal way" best would be to have a space-shuttle-like (winged) spacecraft approaching in near-tangential trajectory going over the atmosphere containment walls. In this case reentry speed should be higher (essentially rotation + "aircraft" cruise speed); as atmosphere thickens spacecraft would become aircraft and lift would start to build gradually.
Minimizing speed difference minimizes also heath dissipation needs.
A spaceship would not normally land on the habitable surface of a bishop ring, given the potential for damage in the event of a failure. In fact, a spaceship would not normally be allowed to even point at a bishop ring's habitable area unless very far away for safety reasons.
Instead, spaceships would dock at an axle-like structure along the station's axis of rotation due to the very much lower delta-V requirements and lower relative velocities involved.
Why land on the ring itself? Is this an emergency?
Your craft presumably weighs a lot more than whatever it is you want to convey to the surface. It has the engines and life support and living quarters. If I lived on a Ring, I would be aware of how potentially delicate it might be. If it tears, all your atmosphere escapes. If it rips through, all your gravity goes. If the ring has been abandoned, you will not know whether it is in good condition. A safer option might be to descend with a space elevator.
The space elevator would be a huge construction for Earth, but is quite practical for a ring. The space raft can be the counterweight. You have the technology for making strong, light fibres as the ring is made of the stuff. You launch a pod on a fibre towards the surface, while turning to match the speed of the atmosphere. You land on the surface and step out. To get back up, the spacecraft reels in the fibre. You may have to use some propellant as the spacecraft-pod system has to gain a lot of angular momentum to land, but the vertical lifting can be done by pulling on the fibre. If the ring accepts visitors, it may have its own elevator module that the craft docks with.
If the ring's atmosphere is Earthlike, the upper atmosphere probably has oxygen radicals that attack the fibre. UV in space would also attack the carbon-carbon bonds. You would probably not want the fibre to be permanently reeled out because it would degrade, but it can stay out for a visit.