Canadian Bouchard had called for Sharapova to be banned for life after the five-time Grand Slam champion tested positive for meldonium at last year's Australian Open, referring to the Russian as a "cheater".
The three-time Grand Slam victor, who memorably triumphed at the All England Club as a 17-year-old in 2004, will not need another wild card in her quest to play at the SW19 qualifiers in Roehampton in June after amassing enough ranking points by beating America's Christina McHale 6-4, 6-2 in the first round of the 2017 Italian Open.
Sharapova came through a hic-cup near the end, losing serve as she prepared to wrap it up while leading 5-1, but recovered in the next game to emerge the victor.
Sharapova was forced to retire from her second-round clash at the Italian Open in Rome because of an injury to her left leg, having took to the court just 30 minutes after Giudicelli's announcement.
Sharapova faces a battle to raise her ranking enough to qualify for the grasscourt grand slam by right and spare organisers the dilemma of whether to award her a wildcard into the main draw of the tournament she won in 2004.
The Russian tennis player, given a wild card to compete in Rome after returning from a 15-month doping ban, dropped serve three times in a scrappy opening set, but won 6-4, 6-2.
"The fact that I'm back and playing three weeks in a row now and three events in a row for me is a big deal".
Sharapova is still waiting to hear if she will receive a wild card entry into Roland Garros starting a week from Sunday; that news will come on Tuesday, when she is otherwise engaged laying her second-round match.
Cash continued: "I would hope they (Wimbledon) would stay strong and say "no sorry, you have got to go through and play qualifying".
Venus Williams, the 1999 Rome champion, defeated Yaroslava Shvedova, 6-4, 7-6 (4).
McHale, ranked 58th, faded badly in the second set as Sharapova hit her stride, producing glimpses of the talent that took her to world number one.
Berdych matched his coach, Goran Ivanisevic, with 599 career victories.
Also, Sam Querrey eliminated Lucas Pouille, a semifinalist previous year, 7-6 (6), 7-6 (8).
Sharapova led 21-7 in winners and committed 22 unforced errors to McHale's 25.
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