The Chelsea loanee had secured the match ball inside 20 minutes against the Conference South champions, managed by former Palace chairman Mark Goldberg.
Sulley Kaikai, Dwight Gayle and Wilfried Zaha were also on target for the visitors, whose forwards responded well to news earlier in the evening that a fee had been agreed for Sunderland’s Connor Wickham.
Academy graduate Kaikai got the first two minutes in, burying a Zaha cross, and Bamford then took centre stage with three in 14 minutes.
The first was a simple finish to Kaikai’s good approach work, the second put away one-on-one and the hat-trick poked in from a Christian Scales centre.
Gayle added a fifth before half-time, and the second half brought just Zaha’s sixth, which came courtesy of a defensive mistake.