As a developmental specialist, I was at first wary when I got to your mention of using food as a distraction. But you knew just what to do. More than a distraction, think about it as something that makes her feel at ease and comfortable - whatever that is, use it to bridge the big step, then phase it out. What worked with my niece was letting her bring her blankie in with her, which was really hard to do from my adult perspective because, you know, "It will get wet!", which is pretty much the worst thing. It is really difficult to solve a fear problem with a 1 year old. Your toddler knows that you care about her and respect her feelings, and she can trust you to keep her safe. Awesome.
Early Childhood Parent/Teacher Trainer Toolbox for Teaching, Washington State
My daughter had the same problem at about 1 year old. For her the fear was getting soap in her eyes. I tried toys, letting her use the big tub, and I even took the doors off the shower in case she was getting cloesterphobic. When I figured out that it was pouring water that was scaring her, I tried keeping in out of her face. Unfortunuatly, a one year old doesn't understand the if she holds her head back, she will get less water in her face.
Finally, I just told her that we were going to do a one, two, three. After her hair is soapy, I warn her that I am going to rinse it out. I count each cup full out loud and pour them quickly. She still freaked out the first couple times. However, once she got the routine down, she realized that after the "one, two, three" there was going to be no more water in her face. She has started to enjoy her baths again.