The British-born Hollywood star told the programme he was "a pikey from Kent", before clarifying that he was not "taking a slant" at gypsy and traveller communities.
After the interview, Bloom said: "I've come from Kent and I grew up with a lot of, like, freewheeling, cool, interesting characters like that.
"I certainly wasn't taking a slant at that at all. I'm very respectful."
Grimshaw told listeners Bloom was "a bit of a loose cannon", adding: "Apologies if you were offended by anything that Orlando may have said."
Radio 1 said: "As with any live broadcast, we take great care to ensure all guests are briefed about their language before going on air.
"We apologised to listeners afterwards for any offence caused."