You can use the ToConstant
method which takes an already existing instance and registers it as singleton.
var kernel = new StandardKernel();
kernel.Bind<MyClass>().ToConstant(myClassInstance);
If you want to something more complex you can use the ToMethod
(where you can use a Func to get your instance) combined with the InSingletonScope
var kernel = new StandardKernel();
kernel.Bind<MyClass>().ToMethod(context => myClassInstance).InSingletonScope();