According to Horace Walpole in his Anecdotes of Painters, a work based on the notes of George Vertue, Bushnell was the pupil of the sculptor Thomas Burman. He spent two years in France, before continuing to Italy. He spent some time in Rome, and in Venice, where he made a monument depicting the siege of Candia and a naval battle for a Procutare di San Marco. He returned to England via Hamburg.
His first works on his return included statues of Charles I, Charles II and Sir Thomas Gresham for the Royal Exchange. He had intended to make a complete set of kings for the exchange "but hearing that another person... had made interest to carve some of them, Bushnell would not proceed, though he had begun six or seven".
Anecdotes concerning his haughty disposition and increasing eccentricity were repeated in artistic circles and recorded in the eighteenth century by George Vertue in his notebooks. One of these stories involves his attempt to prove that the Trojan Horse was not a fable but a practical possibility. He is said to have spent £500 on constructing a timber horse, its head capable of seating twelve men, but it was wrecked by a storm before it was completed, and Bushnell was too disillusioned to continue with the project, although two vintners, who had contracted to use the horse as a drinking-booth, offered to pay for its reconstruction.
Following his death in 1701, his widow Mary and his sons continued to live in his half-finished house near Hyde Park, London after his death, keeping at bay strangers curious to see his remaining sculptures, and by degrees destroying them. A monument, probably his last, is in the North Chapel of St. Andrews Church, Great Billing in Northampton. it is possible that this was moved here unfinished following his death.
In the mid-nineteenth century Bushnell's reputation stood high enough for an imaginary portrait representing him to be included amongst the world's great sculptors in the Frieze of Parnassus on the Albert Memorial, in Kensington Gardens in London.
- Monument of Alvise Mocenigo, S. Lazaro dei Medicanti, Venice, 1663
- Charles II and Catherine of Braganza. Standing figures on Temple Bar, London, 1670.
- Funeral effigy for the Duke of Albemarle's funeral in Westminster Abbey, the face and hands in wax, the robed figure in stucco, 1670.
- Funeral monument of Henry Stanley, Little Gaddesden, Hertfordshire, 1670.
- Charles I, Charles II, and Sir Thomas Gresham for the Royal Exchange, 1671. Conserved in Old Bailey.
- Monument to Abraham Cowley (died 1667), Westminster Abbey, 1674.
- Monument of William Ashburnham and his wife, Ashburnham, Sussex, 1675.
- Monument of Lord Mordaunt, Fulham Parish Church, 1675.
- Monument to Elizabeth, Lady Myddleton, and two portrait busts of Sir Thomas and Lady Myddelton, Chirk Parish Church, Denbighshire, 1676.
- Monument to Lady May, Mid-Lavant, West Sussex, 1676
- Monument of Sir Palmes Fairborne, Westminster Abbey, 1686.
- (attributed) Monument of Lady Henrietta Wentworth, Toddington, Bedfordshire, 1686.
- Monument to the Earl of Thomund, from the Sarah, Countess Dowager of Thomund, possibly his last work, St. Andrews, Great Billing, Northampton, 1700.