Fixing Punctures / Puncture Repair / Exploding Tubes

Changing a flat should be simple. Alas it appears I can't do it right.

Recently I have twice had the tube bubble out from between the rim edge and tire thread and go pop mid ride. It looks like I have done it right, but the first I notice is when I'm out riding and for a few seconds before it goes pop the ride feels a little lumpy.*

thought I would point out in case it is relevant to your situation - this happens if you are using older (non-clincher) rims, when run above a certain pressure. This problem is often seen on 27" rims which are still in use on a lot of bikes from 1970s and earlier and were generally AFAIK non-clincher (mine are).

I solved it for myself (after searching on here, credit where credits due) by just running at a lower pressure, i.e. not going over 60psi at front and 50 at rear, and have not had the problem since. Happened to me during or just after inflating, would not have wanted it to happen while riding.