I agree with Scarlett that you do need a therapist who works with kids and who is experienced at handling kids who have been bullied. If you're referring just to the school counselor, I think school counselors are great, but it sounds like your daughter could use some individual, outside counseling or therapy for a while to get past the bullying and school change issues. I hpe that's what you're getting for her.
You say she's in a new school; I'm not sure if that's just because it was time in your school system for her to move on with her whole grade or if you moved her due to the bullying but I'll assume the latter since you say "she was bullied in public school" so maybe she's iin a private one now.
Just be certain she has time to adjust, without so much academic, hurry-up-and-get-it-done pressure, to the new school. She may be less thrilled with the change than you would expect her to be. "You're going to a new school where you won't see the bullies" may seem great to the adults but even though she was bullied at the old school, it was a familiar place if not a happy one. Adults don't always understand it, but kids truly will sometimes prefer the familiar but unhappy to the new and totally unknown. She may seem "beaten down" and be keeping a low profile because she fears new bullying, no matter how good you tell her the new school will be for her. A good therapist will understand this and help her work through it.
Have you talked all this through with her new 4th grade teacher? Does the teacher realize that she has had these issues and is in counseling and has issues with open-ended questions etc.? Have you talked with the teacher -- first, just you and your husband, without your daughter there -- about strategies the teacher can offer both to help you help your child at home and to work with your child differently in class, so the classwork gets done and not sent home as much? If the new 4th grade teacher isn't williing to listen, understand, and work with you, you should talk to the school counselor and the principal. Ask for a meeting that includes the teacher, school counselor and principal all together in one room with you if the teacher won't help. Don't let them put you off or just say "Oh, the counselor deals with that." You may end up needing some academic adjustments like an individual educational plan (or whatever it's termed in your district) for your child.
Also, I'm concerned that there's so much emphasis in the post on what your child is expected to do in "the class at church." Do you mean a weekly Sunday school class? If so, why so much pressure there? If she's being told to do writing or worksheets and it's stressing her out there, I'd tell the teacher what's going on and to frankly lay off. If it's something more than a weekly Sunday school, once-a-week Christian education class -- why is your child doing that if she's already under pressure with regular schoolwork?
Your child should find church a haven where she can be herself and not feel any of the pressures that she feels Monday through Friday in school; if she's getting the same "You need to finish your work" at church as well, church just becomes a source of more pressure for her, not a place she will learn, just another place she feels rushed and pressed. There are more creative ways for a Sunday school teacher to teach than by pressuring an already fragile kid.
The fact that the church teacher "complained two weeks in a row" as you write -- that's a red flag to me that the teacher may not be able to deal with your child right now. I would talk privately to that teacher, explain that your child is both very slow and meticulous AND under a great deal of pressure with a school change and getting over bullying, and let the teacher know that whatever method she's using does not work for your child and adds to the stress your girl's already under. If the teacher can't find another way to teach your daughter, consider pulling her from that class maybe for the fall. If her church friends are in the class and your daughter really wants to be there, see if you can volunteer in the class or otherwise intervene so church is a pleasure and joy and comfort to your child -- not a repeat of school pressure. I'm active in our church and can't bear to hear about a teacher complaining about a kid not doing some kind of "schoolwork" fast enough. There's no exam at the end, and the teacher isn't going to be judged on whether your child completes some assigment -- is she?