Bencic, 18, clinched her maiden title on Saturday while denying ninth-seeded Pole and 2012 Wimbledon finalist Agnieszka Radwanska a second title at Devonshire Park on the English south coast in a contest that lasted over two hours.
Bencic defeated Radwanska 6-4, 4-6, 6-0.
The native of Flawil in the canton of Saint Gallen was playing in the third final of her career.
She was beaten this month in a grass-court final in the Netherlands by Italian Camila Giorgi.
Bencic got away to an untouchable treble break on Saturday in the third set for 5-0 as she finished the job against the 2008 Eastbourne champion with a forehand winner to the corner.
On Monday, she is matched against Bulgarian Tsvetana Pironkova at Wimbeldon's court 18, starting at around 3pm.
Described by some as Switzerland's new " Martina Hingis", she has been coached for several years by Hingis' mother, Melanie Molitor.
Bencic, who made her debut at Wimbledon last year, was knocked out in the second round.
Now ranked 21st in the world, she is hoping to better that performance but is careful not raise hopes.
"I have nothing to prove at Wimbledon," she told reporters.
"I just want to play relaxed and be satisfied with the results."
Hingis, who began as a teen sensation and went on to win five Grand Slams, including Wimbledon, will return to the courts southeast of London in doubles competition.
At the age of 35 she will be seeking a tenth Gland Slam victory in doubles.
Compatriot Stan Wawrinka, currently ranked fourth in the world, also starts his Wimbledon bid on Monday.
The French Open champion will square off against Portuguese João Sousa at central court at around 6pm.
Other Swiss players — Roger Federer, Timea Bacsinszky and Stefanie Vögele — will enter the first round at the All England Lawn Tennis Club on Tuesday.