I'm doing analysis (dynamical systems) in the context of Riemannian manifolds of bounded geometry and I find myself reproving quite a few standard results/tools from standard differential geometry, such as locally finite covers and subordinate partitions of unity, a tubular neighborhood theorem, smoothing of submanifolds...

The main difference from the standard results is that I require uniformly bounded estimates, so for example the tubular neighborhood must have a uniformly finite size and a uniformly bounded diffeomorphism. This means that I cannot simply generalize the standard proofs.

I'm not familiar with bounded geometry. The only reference with explicit details I found is Schick: Manifolds with Boundary and of Bounded Geometry where a uniformly locally finite cover with subordinate partition of unity is proven.

Are there other books or articles which include similar results in the context of bounded geometry?