Aston was a bastard son of Thomas Aston. Scottish sources spell his name variously as "Aschetone", "Aschetoun" or "Aschingtoun". After serving the Earl of Lennox, Lord Darnley, and Mary, Queen of Scots, Aston was made a Gentleman of the Bedchamber to James VI of Scotland in 1578. In England he was Master of the Great Wardrobe to King James I in England. He held both positions until his death. From 1595 he was keeper of Linlithgow Palace, and one of his daughters was born at the palace in October 1595. In July 1582 he was sent to Antwerp with a Scottish diplomat. They were to bring back Colonel William Stewart of Houston. Aston wrote to the Earl of Leicester describing his mission, the state of Scotland, and reporting the surrender of the town of "Houdencke", meaning Oudenaarde, whose garrison was allowed to retire with ensigns displayed. In December 1586 he rode to London with Robert Melville and the Master of Gray who were sent as ambassadors to plead for the life of Mary, Queen of Scots. He received £4,000 from Queen Elizabeth for James VI, the payment of an annuity or subsidy. Aston brought the news of Mary's death to James VI in February 1587. Archibald Douglas had advised William Davison to delay sending Aston to Edinburgh with the bad news, which could affect Aston's standing with the king, and so his use to English service. However, Aston's reputation did not suffer. In July 1587 Aston wrote to Francis Walsingham and Archibald Douglas from Falkland Palace. He told Walsingham he felt abandoned and wished to seek his fortune elsewhere. To Douglas he wrote of his hopes that Elizabeth would work for James, and of his efforts for Douglas personally in the "part of a true friend". He felt unable to write to their friend Thomas Fowler because of his evil fortune. Douglas sent Aston's letters to Walsingham. It was expected that Aston and Sir William Keith of Delny would lose their places at court because they had been supporters of the Master of Gray, who was out of favour. The Earl of Huntly's followers called Aston, Keith, and the Lord Privy Seal "Queen Elizabeth's pensioners". Aston felt he was watched as an Englishman and could not write as often as he wished. Aston remained in the king's service, and in December 1588 stayed at Kinneil House and played a card game called "maye" with the king. Aston wrote to James Hudson that James was pleased by the news of the deaths of Catherine de' Medici and the Duke of Guise. He mentioned the worth of Fulke Greville's opinions. He was himself growing weary of the "little certainty in this state as I know not what to say to it". James Hudson sent Aston's letters to Walsingham. In March 1589 Aston wrote of his support for the Chancellor of Scotland, John Maitland, 1st Lord Maitland of Thirlestane. Aston went to London and met with Walsingham on 12 April. Fowler wanted his correspondence kept secret from the Scottish ambassador and Aston. Aston returned to Edinburgh on 28 May 1589. In August 1589 Aston travelled to London to buy items for the arrival in Scotland, the wedding, and the coronation of Anne of Denmark. He visited or wrote to Lord Scrope at Carlisle for actors from the Queen's Players to perform in Edinburgh. However, bad weather prevented Anne of Denmark from sailing. Aston travelled to Norway and Denmark with the king in 1589 and 1590. He was made keeper of Linlithgow Palace and once for a practical joke hung a copy of his family tree in the gallery next to that of the king of France, which James VI found very amusing. In 1594 he repaired the roof of Linlithgow Palace using lead shipped from England. While he was at Stirling Castle in September 1595 he sold a hackney horse to James VI for him to ride, costing £200 Scots. He asked the English ambassador Robert Bowes for a fair and large portrait of Queen Elizabeth. Aston kept up a correspondence with Sir Robert Cecil. His letters were sensitive, and once when they were intercepted in England and returned to Scotland he risked disgrace. Probably, James VI knew what Aston shared with his English correspondents, and found this a useful source of information. In 1598 Aston had hoped to buy land for his wife and children's future in Scotland, but was caught up in the financial crisis caused by the bankruptcy of Robert Jousie and Thomas Foulis. He was injured in a fall on the steps outside Anne of Denmark's bedchamber at Dunfermline Palace in March 1602 and was unconscious for three hours.
Aston married firstly Mary Stewart, gentlewoman in the household of Anne of Denmark, daughter of Margaret Stewart, Mistress of Ochiltree and Andrew Stewart, Master of Ochiltree, with whom he had four daughters: