We propose a method for solving the strong form of the dynamic Cosserat rod clamped-free boundary value problem (BVP) under frictional contact. The shooting method is employed for BVP solving, and contact response is computed using the penalty method. The proposed method is tailored for accurate and rapid simulation of catheterization like medical procedures. Our contact scenarios involve complex shapes and real patient geometry, modeled with implicit surfaces as blobby models. The results show that using blobby models for contact detection is orders of magnitude faster than using triangle meshes. This approach provides smoother contact forces, accelerating the convergence of the shooting method. We have made our code available as open source at https://gitlab.inria.fr/rjilani/IROS2024/.