How would you design a saddle for a giant turtle (think rhino size) and a bridle, and how would you make it go, given that spurs or whip wouldn't really be an option with the shell?
Turtles as a mount certainly wouldn't be fantastic for cavalry, but they may make ok pack animals.
To start with a Saddle. Think of the saddles and big curtained affairs that go on elephants. Have the straps go around from front right to rear left and the opposite on the other side. The round nature of the shell should help maintain tension so the saddle or chair or whatever doesn't move around much. The turtle isn't going to be running at a gallop, so this should be fine.
Next your bridle. This is harder. Since most turtles have a beak like affair, you would seriously have trouble with a traditional bit like is used with horses. In a horse, the bit fits in the tender part of the mouth behind the teeth. I don't know that much about the skull and musculature of a turtle's mouth, but beaks might be like giant shears. Sadly, that means we might have to get inhumane. You know the trope about the ring in a bull's nose? That was used as a control and lead point because it hurt the bull to pull against the ring. Find a spot on either side of the turtles head that is sensitive and pierce it to hold the reins. Maybe along the lower jaw or something.
As a spur, you could use something like a prod to reach to the back legs. Maybe a mechanical contrivance that can poke up underneath the shell to the back legs. That way the poor fellow can't just tuck himself up under the shell to stop the poking.
A turtle isn't going to be able to pull huge loads, but they can probably lift quite a lot. Build an area like a truck bed connected to the saddle part to carry cargo.
I hope you can find some very patient trainers.
You don't provide any context on the type of Tortoise you are referring to but something that might make it feasible is long neck tortoises/turtles these animals have necks so long they can't be retracted into a shell or only partially retract.
So you can have classic saddle like you would for a horse mounted on the neck but as these necks are usually used for snapping at things such as with a snapping turtle they would have enough muscle strength to support a rider but if it decided to snap the rider would have a terrible time.
With this long neck style tortoises you could also strap a saddle to the edge of the shell, perhaps something like a camel stool saddle and use extended steering ropes (not too familiar with harnessing terminology) to pull the head side to side to guide the animal in the direction you want to go. This style of harnessing should also work with the shorter neck variant of tortoises or turtles.
The saddle would be like a full chair, strapped all the way around the turtle. If the turtle has a good hard rim around the top shell, you might be able to hook the straps onto that, and tighten them against straps hooked on the opposing side.
It might be best to motivate the turtle with food on a stick, but turtles also have sensitive shells, so "spurring" it might not be totally out of the question. You could touch the rear top of the shell with a hot poker, or you could set something up so that when the rider pulls a cord, a spike is driven into the rear underside of the turtle's shell, prompting it to move away from the harmful spike underneath it.
The shape of a turtle's shell is also heavily affected by the turtle's nutrition intake as it grows. For many breeds, malnutrition leads to a more spiky looking and less rounded shell. That spiky shape might make it easier to keep straps in place, so a turtle being raised for mount might be kept on a careful diet while growing, and then fed an improved diet for strengthening the turtle when it gets big enough to ride.
Turtles' natural defensive behaviors would make them a suboptimal mount for battle. Turtles can be fast, but they also tend to be contemplative. It may just be the case that anyone mounting a turtle must also be patient, and ok with the turtle making random stops here and there.