The LNAB of Alice has only recently been discovered and published.  Among the numerous suits she was involved in are references to grants she made to her brother, John de Salisbury. Her ancestry otherwise remains unknown.
Most older sources presume her LNAB was Perrers, and speculation revolves around which Perrers family she could have come from. Besides the new discovery that she was in fact a Salisbury, we know she could not be a Perrers from documents which call her "Alice Perrers, widow" indicating Perrers is a married name. She was the wife of John de Perrers of London.
Born: Before 1340.
We have little precise information to narrow down the birth date of Alice de Salisbury. The date of 1348 used on Wikipedia, however, is clearly much too late.  We know that she was married and with a child to John Perrers by 1360 and that she was his executrix and widow by 1362. It is stated that she was "long in the household" of Queen Philippa in 1366. Her children would appear to have all been born in the early to mid 1360's. This all makes a best guess of her birth date as say 1330 to 1340.
Marriages and Children
Married:1st - John Perrers of London. He was last known living on 24 June 1360. 
Married:2nd - Sir William de Windsor, Deputy of Ireland between Nov 1375 and April 1376. In November 1375 a jury confirmed her as single. He d.s.p. on 15 Sep 1384/5 Heversham, Westmoreland. 
Mistress of Edward III: She had a well-known affair with Edward III between 1363 and 1374. She acquired significant land holdings from this affair, but she was tried for corruption, banished and her goods forfeited, after the king died.
Children of John Perrers and Alice de Salisbury:
Joan Perrers. One of two daughter of Alice named Joan/Jane. She is sometimes said to be a child of Edward III, but she was not greatly enriched by Edward the way her two siblings were. She married 1st - Sir Richard Northland before 1401. She married 2nd - Robert Skerne before 1405.
Children of Edward III, King of England and Alice de Salisbury:
John de Surrey (or Southerey), knt. In 1374, granted by Edward III an annual maintenance of £100. Knighted in April 1377 along with the future kings Richard II and Henry IV. Granted multiple manors and lands in multiple counties by the king in 1377. He apparently died without issue before his mother (before 1400). Cawley states that he may been married to Matilda "Maud" Percy, daughter of Henry Percy, 3rd Baron Percy and Mary of Lancaster. The source for this is unknown and is not followed by Richardson. 
Joan de Surrey (or Southerey). One of two daughter of Alice named Joan/Jane. In 1394 , as Jane daughter of Alice Windsor, petitioned the king for recovery of £2000 owed her from the sale of the marriage of the Earl of Nottingham. She married before 14 May 1406 _____ Despaigne. She inherited her mother's estates, some of which as "Jane Despaigne otherwise Southerey" she released for a life rent of 100 shillings.
Note: This construction of the marriages for two daughters named Joan is given by Richardson in his Royal Ancestry. Cawley notes sources which would make Richard Northland and Robert Skerne marrying different Joans. However, property records show that Robert Skerne married the widow of Richard Northland. Richardson's construction is far more likely.
Died: Shortly before 25 November 1400.
Date of administration of her estate.
Will: Died testate. Will dated 20 August 1400. Will proved on 3 February 1400/1.
Burial: Will requested burial at the church in Upminster, Essex.
ante. Oct 1366: domicella cameræ Reginæ - lady-in-waiting to Philippa of Hainault.
The first incident definitely known about her is that she had entered the service of Queen Philippa as domicella cameræ Reginæ before October 1366.
↑ Palmer, Perlustration of Great Yarmouth, ii. 430; Blomefield, Hist. Norfolk, i. 319, xi. 233; 1376 m. or betrothed (Chron. Angliæ, p. 97); Also said to have been his wife well before Dec 1377. (Rolls of Parliament, iii. 41b)
RJ, per Richardson who makes a good argument, Robert Skerne married her first daughter Joan Perrers, and not the daughter Joan who was the illegitimate daughter of Edward III. This is different than is commonly found as the name of her first husband has only recently been discovered.