My 11 year old daughter (and 14 year old son) are usually in bed around 9:30. Son actually tends to go to bed before 9:00 (his choice).
But then, they have to be out of the door and waiting for the bus BY 6:45 a.m. and they have a very long day of school. (14 yr old isn't dismissed until 3:45 pm).
When they had a later "out the door" time for school in the mornings, and they were younger (1st and 4th grades?) I had them in bed by 9:00 pm. I always shot for 8:30, but as long as the lights were out before 9:00, I considered it mostly a success. But, they didn't have to leave the house in the mornings until about 7:40.
If your child is not a morning person, it is a challenge for sure. It usually means they have a harder time falling asleep at bedtime, and then of course aren't ready to get up in the morning. What is the issue with bedtime? (besides "dragging") Is there not enough time after dinner for a bath and then to wind down? Can you move dinner up? Have them get their bath before dinner? Have them get ready for bed as soon as dinner is over and then they can "chill" until time for lights out?