However, stand-in Australia skipper Josh Inglis insisted his young squad were ready to bounce back after Pakistan beat Australia 2-1 in an ODI series this month.
"This is a great challenge and a big opportunity - we haven't played Australia for a long time," Mehidy said before the first match at Mirpur on Tuesday.
"Everyone is in good form... If we can perform at our best, we can get a result," he said.
Australia arrived without captain Mitchell Marsh and Travis Head, and Inglis acknowledged that their absence hurt.
Both players also missed Australia's defeat in Pakistan last week, with Marsh nursing an ankle injury and Head on personal leave.
"I think it's really important that a few younger guys are getting some experience in these conditions," Inglis said.
"There's a World Cup on the horizon, so being able to look at different combinations before then is really important."
Bangladesh have won just one of 22 ODIs against Australia. However, Mehidy said their confidence was high after winning three successive series against West Indies, Pakistan and New Zealand.
Home conditions would also play to their strengths.
"Mirpur doesn't have to mean a bad wicket," he said. "If we can win on good wickets it builds confidence -- and that's important with the World Cup coming."
Inglis, who played IPL cricket in India this year, said Australia would reserve judgment on the surface until closer to the toss.
He said conditions could be more seam-friendly than expected based on Bangladesh's recent home series against New Zealand.
"We'll do our homework, look at the games played here recently, and make a judgment," he said. "We're ready for anything."
Both captains flagged Bangladesh leg-spinner Rishad Hossain as a potential match-winner.
Inglis, whose side includes several players familiar with Rishad through the Big Bash League, said Australia would prepare for him carefully.
"He's a very good bowler -- we'll definitely be having some conversations about him," Inglis said.
Bangladesh and Australia play three ODIs on June 9, 11 and 14 and then play three T20s.