A source tells PEOPLE "Katy is happy with Orlando"
Credit: Bruce Glikas/FilmMagic; Jason LaVeris/FilmMagic

Katy Perry and Orlando Bloom‘s romance continues to ramp up.

The pair – who ignited relationship rumors at a Golden Globes bash in January – have been busy jet-setting the past month.

After enjoying a late February Hawaiian getaway, the singer, 31, and Bloom, 39, flew to the English actor’s homeland on March 5 to visit his friends and family, including his mom Sonia.

For more on Katy Perry and Orlando Bloom, pick up the latest issue of PEOPLE, on newsstands Friday.

And when they’re back in L.A., a source tells PEOPLE Perry is spending more time getting to know Flynn, Bloom’s 5-year-old son with ex-wife Miranda Kerr. Perry first met the tot in February before joining him and his dad at Robert Downey Jr.‘s son’s birthday party.

The source says Perry’s time spent with Flynn is seemingly indicative of how serious their relationship is.

“Orlando is very protective of his son,” says the source. “To introduce Flynn to Katy, she must mean [a lot] to him.”

Indeed, a friend of Perry’s tells PEOPLE: “Katy is happy with Orlando and more ready to settle down.”

With reporting by LIZ McNEIL