The U.S. supreme court has ruled that all navigable rivers and streams are public , including the river bank up to the high water mark. But many states ,....like the one I live in follow "common law" , upholding and enforcing that the "water only" is public , and that the river bed in fact belongs to the respective property owners. People have fought this in states like Utah , I believe and won but at considerable effort and cost.
Depending on what state you live in the river/creek bed may be private property even if navigable , regardless of the federal navigable waterways ruling , ....its just a state thing.
I am looking at property in Virginia. One of the qualifications for it is that it must have a creek or flowing water through the property. With that... one of the questions I asked to the realtor was exactly about this.
The laws change and can not only vary by state, but local laws as well.
Most property lines stop in the middle of the water source (River, creek, etc.)
The definition of 'navigable' also varies. However, the issue is that there is no definite high water mark in some places. Navigable in laymans terms is simply floating the river. Once you step outside of the floating device, boat, kayak, etc. you can be trespassing. If the creek is NOT capable of supporting a boat or kayak, it is deemed not navigable and is considered private property.
A BIG PROBLEM:
One of the biggest threats to this very existence of law is the issue of liability. If you're on my section of property on the river or not and you or someone gets hurt, killed, etc., then there are liability suits for the property owners. As crazy as it sounds, it happens often. This very issue is often why property owners do not like having people hunt or even metal detect on their property because of the liability. Waivers or not, it's an issue.
To the original poster, Virginia specifically is middle of water source, unless property owner owns both sides of the water source. So as long as you're in your boat, you can travel through. Remember, if you're in a state park or federally protected area, relic retrieval is illegal regardless.