Pressley was born into a racing family in Asheville, North Carolina; his father, also named Robert, was a short track racer in the area. His brother Charley built a long career as a NASCAR crew chief. Pressley came up through the ranks at New Asheville Speedway and Greenville-Pickens Speedway, winning championships at both facilities and eventually amassing more than 150 wins across various Late Model Series in the Southeast.
Pressley made his NASCAR Busch Series debut at Charlotte Motor Speedway in 1984, finishing 26th. He returned to the series on a limited basis, and in just his 12th career series start — at Orange County Speedway — he took his first win. Running full seasons from 1991 to 1994, his best campaign came in 1992 when he won multiple races and finished fifth in the Busch standings. In 1994, while still primarily a Busch driver, Pressley ran three Winston Cup races in a car sponsored by Manheim Auctions, with a best Cup finish of 31st at Charlotte Motor Speedway.
A notable incident occurred in 1990 at Bristol Motor Speedway, when Pressley was involved in a crash that sent Michael Waltrip into the pit gate wall, nearly destroying Waltrip's car on impact.
In 1995, Pressley stepped into the Winston Cup full-time, replacing the retired Harry Gant in the No. 33 Chevrolet for Leo Jackson Motorsports. He posted one top-ten finish that season and finished as runner-up to Ricky Craven for the Winston Cup Rookie of the Year award. In 1996 he improved to two top-five finishes, but when Leo Jackson sold the team to crew chief Andy Petree, Pressley was released after a single race.
He landed a ride with Diamond Ridge Motorsports in 1997, running 10 Cup races including the Daytona 500, where his car famously flipped nose-over on its roof in the opening laps. He was soon released mid-season. He moved to the No. 77 Jasper Motorsports entry, which became one of the more consistently popular teams with fans on the circuit.
Pressley returned to Jasper full-time in 1998, producing a career-best third-place finish at Texas Motor Speedway, though a mid-season injury necessitated a temporary replacement by Hut Stricklin and he ended the year 32nd in points. The 1999 season was difficult, with six failures to qualify and persistent mechanical issues; he finished outside the top 30 in points. With the addition of engineer Ryan Pemberton in 2000, Pressley climbed to 25th in points. His most competitive Winston Cup stretch came in 2001, when he recorded five top-ten finishes, narrowly missed winning the inaugural Tropicana 400 at Chicagoland (finishing second), and ended 25th in points. He parted ways with Jasper at the end of 2001. His final Cup start came at the 2002 Daytona 500 with Melling Racing, which he secured by qualifying fifth overall on Pole Day; the race ended with engine trouble on pit road.
At the start of 2002, Pressley joined Bobby Hamilton Racing in the Craftsman Truck Series and won his very first truck series race at Daytona International Speedway. He moved to HT Motorsports for 2003, finishing 12th in points, and returned to the Busch Series alongside truck starts for the remainder of his career, with a final truck standings of 20th in 2005.
Pressley served as promoter of Kingsport Speedway in Kingsport, Tennessee from 2011 to 2014, transitioning the track to NASCAR Whelen All-American Series–sanctioned status. He owns Celebrity's Hot Dogs restaurant in Asheville, North Carolina. In 2016, he was elected as a county commissioner in Buncombe County, North Carolina, a position he held through 2022. His son Coleman won the 2010 UARA-Stars championship and later became the spotter for NASCAR Cup Series driver Joey Logano. His nephew Caleb Pressley became a well-known blogger and podcaster for Barstool Sports.