Four properties were targeted between 22:00 on 8 July and 05:00 BST on 9 July.
A 19-year-old woman from Bedford arrested at the time has been bailed.
Three men aged 19, 21 and 22 were arrested on suspicion of firearms offences on Sunday and bailed. A further 19-year-old man arrested on Monday remains in custody.
The first shooting was at 22:00 in Faraday Square, in which a woman was shot in the arm and taken to hospital with non-life-threatening injuries.
Shots were then reportedly fired in Lovell Road at about 01:00, Foxglove Way at 01:20 and in Romsey Way at 05:00. They are being linked by police.
Bedfordshire Police said they "may have been targeted attacks".
Det Insp Katie Dounias said: "The investigation is on-going and we will pursue a number of lines of enquiry.
"We are continuing to urge the public to come forward with any information they may have about the shootings."
Four more people have been arrested in relation to shots being fired in Bedford at the weekend.