After Ripleys testimony and before they even go out, Burke has probably figured out what's going on. And we later find out he is indeed responsible for what happens to the colonists. He definitely has his ulterior orders/plans already. And it isn't until Ripley pieces everything together and tries to expose him that he turns against her.
So why would he need Ripley to come? Why would he even want her there?
She still possessed worthwhile knowledge on the creatures.
You've also got to remember that Burke massively underestimated them. He assumed the marines would be able to deal with them.
She did have a lot of knowledge about the alien. But too bad that the Marines placed more faith in their weapons than in Ripley's firsthand knowledge.
I also think Burke figured that Ripley would be his ally in bringing back some live aliens. He wrongly assumed that she would be happy to assist him in smuggling back the eggs and "we will be set for life". She had lost her license and he figured that she would be happy to make money off the aliens.