Evelyn, Have been doing some more digging on behalf of you and Charles Bush. From several Lancaster Co., Record Books I have at hand: (Abstracts only)
Peter Bush md. Alice Riveer on 10/19/1794 in Lanc. Co., with Peter Rivere as security.
Peter Bush was named as a son of James Bush in James' 1765 Lanc. Co Will (WB18:67). That will dated 1765 and proven 1766 also mentions an unnamed wife and children but specifies a son Peter Bush. James names Peter Riveer as his Executor. The will was witnessed by John and Judith Hazard and John and Joanna Riveer.
When James Bush's Estate was divided in 1782 it mentions that Margaret Bush was dec'd. Was she James' wife (aka Margret Riveer?)? Estate divided between James and Peter Bush, Peter Riveer, Peggy Mason, Betty and Nancy Bush.
It would appear from est. division that James Bush was the f/o Peter and James Bush and several daughters. I believe Peter Rivere may have been the brother of Alice Rivere Bush.
The witnesses on James Bush's will included John and Joanna Riveer. Both James Bush AND John Rivere resided in Christ Church Parish at the time of their wills.
Peter Rivere was referred to as son in law in James Bush's will. Had Peter Rivere also md a Bush??? He obviously was close to James Bush to be named as his Executor.
I believe Peter Rivere and Alice Rivere Bush were John Rivere's children.
Will of John Rivere, Sr. of Christ Church Parish, Lanc Co. dated 1/24/1775, proven 6/18/1787 (WB 22:151) Names wife Joanna, sons Peter, Wyatt, Richard, Bushrod and John and dtrs as Amy, Agnes Rivere, Hannah Webb and Sarah Brown. Executors as wife, brother Johnson Rivere and son Richard Rivere.
There is a tad more info from John Rivere's will. He had a brother named Johnson Rivere. This might indicate that their mother had been a Johnson or not.
Also found that an earlier Peter Rivere died sometime ca 1737 and an Inv. for his estate was done in 1737 in Lancaster Co with George Brent as administrator.
FYI: Richard Goodridge seems to play a close role in the Rivere family. I would check out that family.