Toddler bathing in tub for first time... a question...?

I have a bad back so I've been bathing my daughter, now 18mo., in her infant tub on the floor of her room since birth. Well, now that she's getting too big I've put one of those squishy mats (anti-slip) in the tub along with tons of tub toys and she FREAKS out! Then again, she's never really been in the bathroom before so she looked around at how big everything is. She calms down, after about 10 - 15 min., but must hold on to the tub rail with one hand at all times. Once we're done bathing, she plays a kicks a bit with one hand on the tub railing. Any ideas on how to calm her fears?