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I am extremely rusty here, but I think you should probably read that as confirmation that even in a worst-case scenario, the image on the left-hand page won't be visible at all on the left edge of the right-hand page.
One factor that comes into play is that the effective gutter in a bound book varies a bit between different pages, aside from normal variance in trimming. Depending on where the page is in each 'booklet' of maybe 16pp, which is a folded and cut single print sheet, the spine will open up a little more or less. But the printer should look after all that, and should alert you if anything in your artwork might cause problems.
It's not quite that simple. The printers will actually arrange the pages to print so they can be bound into a book (imposition). So if there was a bleed, it wouldn't be from a left-hand page to its following right-hand page, but might be from e.g. page 4 to 13.
The 'gap' between bound pages (which is hidden in the binding, or is cut off in perfect binding) is a 'gutter' - although that has more than one meaning. You should generally bleed an image into the gutter to prevent white space at the spine in the finished book. Printers should prevent this from actually bleeding to another page as part of pre-press.
Check with your printers though....