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Bouchard stormed into the limelight in 2014 when she reached the semi-finals of the Australian Open and French Open, as well as the final of Wimbledon, but since then she has struggled to make her mark.
In Melbourne on Wednesday, Bouchard started strongly as she went a break up in the first set, but Radwanska responded immediately with a double break.
The Polish pro had to fight for a set point as she squandered four opportunities, but she eventually made it and took a one-set lead in just under 50 minutes.
Radwanska kept the momentum as she snatched serve at the first time of asking and Bouchard failed to respond as she lost serve once again.
It took just 36 minutes for Radwanska to wrap up the set and book herself a spot in the next round.