Spain were playing their first game at home after winning the World Cup in Australia last month and following the furore caused by former Spanish Federation (RFEF) boss Luis Rubiales kissing player Jenni Hermoso on the lips at the medal ceremony.
The fans showed their support for the world champions, with captains Alexia Putellas and Irene Paredes showing off the World Cup trophy to the 14,194 fans at the Nuevo Arcangel stadium in Cordoba, setting a new Spanish attendance record for the women's national team.
"We were looking forward to celebrating with the fans," Bonmati told TVE.
"I'm happy with the game, with how we won and with the attendance record. It's a night we will never forget."
Lucia Garcia and Putellas both had good early chances to open the scoring from close range denied by Swiss goalkeeper Elvira Herzog.
However, Herzog made a comical error a few minutes later, losing the ball inside the box to Mariona Caldentey, who put it on a plate for Garcia to tap the ball into an empty net and give the hosts the lead in the 14th minute.
Spain kept up the pressure but it was not until first-half stoppage time that they managed to extend their lead after Putellas brilliantly passed to Olga Carmona on the left wing, who crossed for Bonmati to unleash an unstoppable right-footed volley into the net.
The UEFA Women's Player of the Year and World Cup MVP scored her second and Spain's third goal with a tidy finish in the 49th minute after a fine individual effort by Putellas, while substitutes Inma Gabarro and Maite Oroz extended their advantage with two further strikes.
With the Nations League doubling as a qualifying tournament for next year's Olympic Games in Paris, Spain are top of the League A Group 4 standings on six points, three above Sweden and Italy, while Switzerland are bottom with two losses in two games.
