The 20-year-old was attacked on the High Street, near Asda, in the early hours of Saturday. He later died of his injuries.
Now two boys, both aged 15, and another boy aged 16 were arrested a hotel in Rhyl, North Wales, on Tuesday night.
They have been brought to the West Midlands for questioning. Two search warrants have been carried out in Walsall as the investigation continues, the force said.
Police added a post-mortem revealed Mr Atkinson, from Bloxwich, died of multiple stab wounds.
Supt Pervez Mohammed, of Walsall Police, said: “We’ve had extra high visibility patrols in and around the areas since the awful events of Saturday night, to reassure the public.
“People will see extra officers over the coming days, and we’re working closely with management at pubs, clubs and bars as we continue to work hard to keep the borough safe.”
Speaking at the weekend, Bailey’s family said “We respectfully ask for privacy at the moment while we grieve the loss of our beloved boy Bailey. Our kind-hearted and much-loved son, brother and grandson.
“Bailey was so loved, by so many and will be missed so much. We request if anyone has any information, they please come forward to help the police with their enquiries to help catch the individuals who done this and taken away our boy.”
An array of flowers, heart-warming pictures and balloons have been laid in Walsall town centre in memory of Bailey.
Anyone with information has been asked to get in touch quoting log 225 of January 28. People can contact the force via Live Chat at west-midlands.police.uk, or via Crimestoppers anonymously on 0800 555 111.