I can't tell if you mean the bounding box or smart guides, or maybe something else. Please tell us your version of ID, and the OS, and provide a better description of whaat you are doing, or post a screen shot.
If you save a document with frame edges showing, the edges will still be showing when you open it the next time. The same goes if you save with hidden edges (they will still be hidden).
You can set whether they will show or hide on new documents by changing the setting while no documents are open. I don't think there is a way to change the setting on existing documents by default, so if the setting isn't what you prefer when you open a document, change it afterward. I work with people who like edges hidden, and I like them showing, so this is something I do all the time. If you use the keyboard shortcut, it will take no time at all.
Bob, Preview Mode also exhibits the "problem" of the OP:
.. thin blue boundaries that show up through the centreline, the moment an object or any image is clicked ..
It appears to me as if the OP does not want to see his selection. I was going to suggest to try and do your work without selecting anything, except that being able to select something (and then do something with it) is a pretty basic function in DTP software.
Bob Levine wrote:
Well, you could set the layer color to white if you’re working on a white background.
You need to come look at the illustration... Changing the layer color would only be useful if the color matches the stroke, and the bounding box is actually inside a stroke.
I get an annoying black rectangle behind my text whenever I select it, and the text color itself changes to its inverse in RGB color space. That makes it quite hard to change the color of some selected text because I cannot see what it actually will look like.
(In case the OP is still following this thread: a solution to this, and his problem as well, is to open an additional window with a view on the same document. You can manipulate a selection in one window, and the other window will update it live while you are doing this. Quite an impressive, yet relatively unknown, feature of InDesign.)