The couple - who have been dating for around four months - were halted by security after the 21-year-old `Camp Rock` star accidentally put some newly-bought cheese knives into his carry-on bag.
Ashley explained: "We were going from the Middle East to New York, so there was tons of security, tons of screenings. We got through one, surprisingly enough.
"The second one we got to and they stopped and looked at us with these really stern faces. They were like, `What`s in your bag?` I look at Joe and there are these flashbacks of this knife set we got. They were cheese cutting knives. I look at Joe and I`m like, `Did you leave the knives in the bag?` He`s like, `Whoopsies.`
"Whoopsies doesn`t cut it. We were going to get arrested!"
After explaining their mistake, the couple were allowed to stow their knives in the plane-s main baggage area.
Ashley added to US TV talk show host George Lopez: "It was embarrassing."
The interview marked the first time Ashley, 23, has confirmed she is dating Joe.
She said: "I have been in Peru, I was in Columbia, Argentina, Chile and then we just got back from Abu Dhabi.
"I was there for pleasure - my boyfriend was on tour and I had some time off so I went out to support him. He`s really sweet."
Travelling from Abu Dhabi wasn`t the first time Ashley has had an unfortunate incident with airport security.
The brunette beauty created problems for her `Twilight Saga` co-star Kellan Lutz after he was forced to travel with her belongings when her suitcase got damaged.
She recalled: "We were travelling together for the `Eclipse` international press tour. We were packing, we`d woken up late and my bag broke, so he told me to put some of my stuff in his bag.
"We go through security and he was picked to have his bag screened. They opened it and out popped everything girly you can imagine. You`re not meant to carry other people`s things so we were trying to explain it without getting arrested.
"I was sitting there finding it hysterical because there was this big guy going through his bag saying, `Heels? Panty hose?` "