Personally, I don't think she went in the water as I feel there are far more likely scenarios. Had there been other clues, of course I'd imagine she was in the water. The lack of skid marks, scuffs, hand marks, dropped or lost items that would come loose during a tumble - earrings, finger nails, hair, buttons, scarf, hat, ear-phones, tears to clothing that would leave bits of fabric behind - all speaks to me that she didn't go in. Plus no-one heard any sudden scream or yelp or calling out.
There isn't any evidence of hard rocks that she would have hit her head on to be knocked unconscious and there's no blood or body fluids have been declared found by LE.
Friends and family say NB was a strong swimmer, plus she was also fit and lightweight. Her jeans were fitted, look thin fabric, not loose, and the jackets either filled with feather down or polyester, those are not heavy materials when saturated as opposed to say thick wools and linens. Her hair was tied back in a pony tail. Her boots were only ankle length and rubber, they would have been lighter weight too, they'd take in water but not as much as bigger boots and they would slip off more easily than tied on shoes or bigger boots. Would those small wellies filling with water and the weight of her synthetic fabric coat which was closely fitted really drag her under? I don't think so IMO.
I imagine tumbling into freezing cold water would be terribly shocking and one would immediately lose breath and then start scrambling to get out, maybe screaming for help. People say the divers needed help to get out, well yes they did because they had heavy diving equipment and flippers on and anyway why would you leave someone to struggle their way out of the river than give them a hand. It doesn't mean the river is impossible to climb out of by default. NB's coat coming down to knee length, if zipped up and pulling downwardly with weight of water, would restrict leg movement for swimming and climbing.
As for the dog, a spaniel who loved water, I believe the dog would go in after her for various reasons. Either to follow, to 'help', or to play alongside if it's daft as a brush. Also if the dog was surprised by a strange kerfuffle of the owner and the owner seemed in distress, the dog would probably start pacing along whining and crying from the bank side.
I think it would take a long time of struggling to get out and maybe yelling for help before one would entirely lose breath and become weak to the point of losing life. JMO MOO