Assuming that scanning is needed to solve the problem of how to avoid collisions with macroscopic objects such as meteoroids or even larger objects, then scout drones with their own warp bubbles might suffice and would be the logical "first thing" to try to develop. The basic idea is that they would scout ahead to detect objects on collision courses with the mothership and on discovery report back by physically returning to the mothership's warp bubble, so that the mothership could make course corrections.If your warp bubble is travelling faster than c, you can't scan ahead of it. However, perhaps some forms of warp bubbles could skitter on top of actual spacetime in a sort of Leidenfrost effect and avoid interacting with objects in it. It would make navigation very difficult.
There would be many problems to solve, such as how to keep the drone cloud in formation with the mothership and with each other and such as how to keep everything in the entire formation situationally aware. Not least among the problems is that each drone, being in essence a starship itself, would cost a sizeable fraction of the whole mothership. Significantly also, drone attrition could be a problem and one that might indicate the presence of a threat.
Active scout drones that could destroy objects without even reporting back in advance would be another possibility with its own slew of issues, not least of which is that it could involve the risk of destroying something that the mission exists to locate, such as evidence of intelligent life.