If you use morph immediately upon it recharging, it will be used up within the space of one or two turns. If you wait awhile after it charges up, the bar will decrease slower, thus allowing you to remain morphed longer.

Oh yes, and if you've gotten Terra back on your party, you should know what she morphs into. Terra is half esper, and she has her normal, human form, and her esper form, which she morphs into when able. Ramuh explained that in Zozo, and the esper Maudin is her father.