With the recent discussion about Bradford birder access, I thought it would be relevant to chime in what I know about the topic.
As I am currently in the field, I am not able to research this as thoroughly as I would like. However, I still believe there is useful information here that would be of interest to potential visitors.
According to Department Engineer for the Delta Water District that Bradford is part of, the island ferry and the main levee road are entirely public property. I am still researching whether or not the roads through the middle of the island are public as well. As long as one does not trespass on private land on the island, which is not necessary to view the vireo or most other birds present, there should be no issues. As Dave mentioned, there are a couple specific individuals who do not take too kindly to visitors, but visiting the island is entirely legal granted one does not trespass.
As for the birds, it is of great import in my opinion to keep close tabs on this/these vireo(s). This is a state and nationally listed taxa, and as such breeding evidence could have a large number of conservation implications for the island. I visited the site on 6/9 and also had a Willow Flycatcher at the same location as the vireo. While almost certainly a migrant, Southwestern Willow Flycatchers, another listed taxa, once bred all the way up to Stockton (per Grinnell and Miller) in the 1940s. Should there be a Willow Flycatcher at this site in a week, it is very much worth keeping an eye out for any nesting activity (may be a bit of optimistic thinking on my end but heck, it is at the exact same spot as a Bell's Vireo...)
Anyway, I just hope none are too disheartened by a couple sour apples on the island. Landowners often, very reasonably, do not like people in the vicinity of their land, but in this case I feel the importance of keeping tabs on and documenting one of the most ecologically and conversationally important species in the Bay Area right now outweighs these concerns of privacy. The levee road is entirely public and any issues the neighbors have are personal and not legal matters. As such it seems reasonable to me that overall conscientiousness and respect towards the residents of the islands should be all that is needed. That said, this argument is moot if people are trespassing or otherwise exhibiting bad behavior, so please stay on the levee when on the island.
In any case, I hope many others get to visit the island in coming months. I was told that if being accosted by landowners ever becomes an issue, this is an problem that should be brought to the board of directors of the island to address. Please do mention if you have any issues with landowners. It would be great to make this situation as pleasant for the birders and residents alike. Ultimately, I believe this location is likely one of the top five or so birding locations in the county and it would be a shame if people did not visit this under-covered gem out of fear of legal ambiguity. Good luck out there!
San Francisco/Willows, CA