I have a few questions. I have kept many dogs and many stupid and many nice, so...Is your doggie good friends with Bella? If, he is then there is something in your garden which disturbs him, some animal or bug which he is spooked of and so can't go outside. If he isn't good friends r just ok friends with Bella, there might be a chance that Bella bit him, but, don't mind me being rude. I said that because I used to have a little lamb or goat kid, whatever.. She used to be in our garden and somehow our dog opened the door and came in the garden and bit her which caused an exactly same mark on her body. It looked ALOT like the mark on your doggie. Try it out, just to see if I'm right:
Oneday, don't let Bella out and just open the door for Jack to see if he goes out or not, if not then there is alot of chance that he doesn't go outside because of something or someone who is disturbing Jack. Try looking around your garden for some signs. And does Jack go outside during the night? Because if he does, he might have got this mark by a night creature, like a badger or something. You check as well just in case you find something.