That particular irrational fear is common. Take her fears seriously, because they're real to her. Explaining that they are unfounded doesn't work, nor does smiling at or dismissing her fears. If you're reassuring and comforting, she'll learn one more reason to trust you with her feelings (really important) and that it's okay to feel afraid. Then you can work on her feelings together.
A washcloth or rubber mat to cover the drain/plug might help. Make a show of covering the drain with the mat before filling the tub. Stay with her for a few baths, and don't drain the water in her presence. Remove the toys from the tub when she gets out so she need not worry about her toys suffering a mysterious fate.
Maybe you can draw and color pictures of plumbing or look at a children's book describing how plumbing works. You can help her draw an imaginary house and include the plumbing. Familiarity sometimes helps to dispel fears (make sure the pipes are small!) Giving her a chance to learn, and talk at a leisurely pace about her questions might help to build a calm rapport about it.
Cooking macaroni (spaghetti can sneak out) and showing her how a colander works when you drain it might help. She might be interested in rinsing fruit, salad greens, etc. in the sink through a colander, or give her toys a bath in the kitchen sink. You can tempt her with bubbles and food coloring in the water and call it a special treat for her dolls. She will learn by experience that things don't go through the colander or the kitchen sink drain, and it will give her a safe venue to deal with her fears.
Bathing her when she's less tired might be less stressful for her.
Through trial and error, you and your toddler will figure out together what helps to increase her sense of power and control over things that frighten her.
Rarely, but it does happen, children can develop a genuine phobia (an intense and persistent irrational fear). It's a good idea to speak with her doctor if the fear persists for longer than a few months, or your child reacts to a fear so severely that she simply can't be calmed.