Quite frequently there is no nearby surface ship. The mission of a ballistic missile submarine is strategic deterence. They bore hole in the water a 4 knots in the middle of the ocean. When there hear a surface vessel on sonar, they turn the other way. If a US Navy surface vessle is close by, it is likely just in transit to somewhere elese.
Fast attack subs can support surface vessels and may be in close proximity to US Navy vessels. They also perform loe wolf type operations such as special operations (spying) and are not even close to US Navy surface vessels (maybe the surface vessels of other countries).