The LottoNL-Jumbo youngster won the sprint out of a six-rider break which saw the 184km stage from Le Chambon-sur-Lignon to Tullins through to the end after establishing itself inside the first 10km.
“I can't believe that I got my first pro win at the Dauphiné,” Bouwman said. “It's a really big race.
“The six of us were pulling very hard. In the last 20km, we believed we could make it.
“My team-mate [Alexey Vermeulen] pushed hard in the front. We're a team of very young guys here. Everyone gets his own chance. Everyone wants to break away.
“Two of us did today and at the end, it was perfect for winning.”
The 23-year-old outkicked Edvaldas Siskevicius (Delko Marseille Provence KTM) and Frederik Backaert (Wanty-Groupe Gobert) while Stage 2 winner Arnaud Demare (FDJ) won the bunch sprint 11 seconds later.
"I'm very disappointed,” Demare said. “Today it was possibly the only stage I was convinced it would end up in a bunch sprint and it didn't. We got fooled by the breakaway riders. They've been very shifty.
"We had three FDJ riders pulling but it meant three against six doing a good job at the front. Other teams reacted but a bit too late. With 15km to go, I realised it was game over.”
Thomas De Gendt (Lotto Soudal) retained his yellow ahead of the 23.5km individual time trial from La Tour-du-Pin to Bourgion-Jalieu on Stage 4.