I love bags and changing bags are no exception!
With DD, I had a Cath Kidson one from John Lewis. I think it was about £60. It had a long extendable strap, so fit over the handles of the pushachir, wipe clean inside (very important, that), lots of pockets so that I knew where everything was and wasn't rummaging, a pocket on the outside (useful as then I could keep my keys, phone and purse and access them without opening the bag) and it came with a changing mat and a bottle insulator. These were less useful I found - the bottle insulator didn't keep a bottle very warm (though it did stop a leaky bottle leaking all over the bag) and the TT proper insulators were much better, and teh changing mat was incredibly bulky and so that didn't work for me. When the baby is small, and you're changing it outsode the home, the mat is the last think you put in your bag. If your bag is full, its harder to fit a bulky mat into ity, especially as you're probably doing this with one hand! Thhis time, I'm going to buy a mat separately that folds down - I've seen some in JoJos.
The CK bag was fab, but teh strap broke after 2 1/2 years of use, which I thought wasn't unreasonable.
This time round, I have bought a Mothercare bag which is virtually identical but for the print. Can't link from here, sorry, but its £45 (was 20% off last week when I bought it) and the print is white, pink, a bit of greenn and a bit of grey. I'm super pleased with it.
I will also get the freebie plain black changing bag free from Boots with its Parenting club.