Not yet found a primary source. Debrett's gives a date of birth and has her as the youngest daughter of Lord William. Burkes also has this
Lord William was an eccentric who was murdered http://www.historyofparliamentonline.org/volume/1820-1832/member/russell-lord-william-1767-1840 )
He was according to the above "b. 20 Aug. 1767, 3rd and posth. s. of Francis Russell, mq. of Tavistock† (d.1767), and Lady Elizabeth Van Keppel, da. of William Anne, 2nd earl of Albemarle; bro. of Lord John Russell"
The National Trust also says that she is Lord William Russell's youngest daughter and has a picture of her as a child (probably not copyright free)
Aha found a more contemporary source mentioning that they were cousins .An 'announcement ' of their marriage
The Edinburgh magazine Vol 26, July- December 1829 p 268
evidence of Wriothesley Russells parents
The Right Hon'ble Lord Wriothesly Russell son of his GraceJohn Duke and Georgianna Dutchess (sic) of Bedford born 11 May 1804, baptised 5th June
St Martin in the Fields, Westminster
London Metropolitan Archives, St Martin in the Fields, Westminster, Transcript of baptisms, marriages and burials, Mar 1804-Mar 1805, DL/T/093/003 (viewed on ancestry)
see also Cambridge alumni http://venn.lib.cam.ac.uk/Documents/acad/2016/search-2016.html
Russell, Lord Wriothesley.
Adm. pens. (age 19) at TRINITY, June 25, 1823. [4th] s. of John [6th Duke of Bedford], Earl Russell (by his 2nd wife, Georgiana, 5th dau. of Alexander, 4th Duke of Gordon).
B. May 11, 1804, in London.
Matric. Michs. 1823; M.A. 1829.
R. of Chenies, Bucks., 1829-86.
Preb. of Windsor.
R. of Streatham, Surrey, 1830-5. Canon-Res. of St George's, Windsor, 1840-86.
Deputy Clerk of the Closet to the Queen, 1850-86.
Chaplain to Prince Albert.
Chaplain-in-Ordinary, 1862-6. Married, June 23, 1829, his cousin, Elizabeth Laura Henrietta, youngest dau. of Lord William Russell, and had issue.
Died Apr. 6, 1886, at Chenies.
(Record of Old Westminsters; Boase, III. 355; Burke, P. and B.; Cant.
Act Book; Lipscomb, III. 251; Crockford.)
(the Chenies village site has some nice info about him as the local vicar .. though you have to remember that Chenies manor and Church together dominate the village which is not much more than a bend in the road between Chesham and Chalfont, the manor of course was owned by the Russells)
Edit, as far as I can they are first cousins