Nick,
Different people have different ways,lot's of conflicting views on Break-in
I like to do similar what you mentioned.I start it up w/ the first few miles and run it decently,make sure to give the RPM's what you normally have,go a bit easy the first ride;down shift a lot.I like to run it hard enough to break the rings in properly.I think it's good to put your hand on the left crankcase cover to judge how hot it's getting... The engine should be shut off when hot and allowed to cool off completely;do that over and over.The thing I think is important is the first 50 miles,the first ride go easy but the 2nd & 3rd one give it more gas and work it progressively more.I like to downshift and rev it towards 6-7(on the way to 8K) on your CB125 (if you have a tach.)and then let off to let the rpms drop.
I think the key is drive it as you normally would but vary the rpm's and let it cool off fully once it's heated up before you go again;don't baby it too much,don't climb hills in a high gear!,keep down shifting and up the rpm's to correctly 'seat' those new rings.I'd ask the machine shop to finish hone w/ #400 grit stones.
That little 125 likes RPM's so break it in the way you enjoy riding;the powerband runs nice from 6500-9500 rpms and that's the 'sweet spot' w/ your bike so get it used to 'powering up' to that regularly. I've owned many CB100/125's and that's what I've done and they worked out best that way.