The public response depends on the targeting the group uses. That in turn depends on the response they want. As such the response to a bombing campaign defaults to "whatever the group doing it wants". How close the reality comes depends on the relative competence of the group and the government managing the issue.
For example most strikes at western targets by Islamic militants have the simple aim of making the group look like "the real deal" so that discontent youth will join the group instead of a competing group or getting a job and family. So the goal is really to get some president or prime minister on television to tell in emotional voice what "evil people and a serious problem" these people are. So the goal is to create an incident that the government must respond to decisively (read: without coherent containment strategy). High death toll of unrelated people, targets of high visibility, multiple simultaneous strikes... All geared to create a strong government response that legitimises your propaganda.
Sometimes the group wants publicity to a specific issue without creating negative opinion. In such cases you attack targets that many people have connection to and might create a high death toll (it could have been me...), but actually try to avoid casualties by timing or warning authorities in advance. This keeps your issue in peoples minds and creates pressure on the government to find a solution.
Some groups wish to stop some specific thing from happening. In such cases targeted attacks on people directly involved are used to create a suppressing effect. The canonical example is various resistance movements targeting collaborators to prevent the occupying force from gaining control of the area. Religious movements attacking doctors, journalists, religious minorities, or schools also happens a lot. The goal is simply to make it harder to find the people who will do the thing you want to stop. In such case, the public response is rarely a serious consideration apart from trying to avoid collateral damage that might create useless complications.
Another possible approach to stopping a specific commercial activity is to make it economically impractical by committing attacks that cause increased costs. This can be either targeted at the specifics of the activity, say destroying data used in breeding programs or disrupting a test program so that it has to be restarted to get valid results, or a generic "cause damage and insurance costs will go up." A group like this can claim to be totally non-violent and make an effort to avoid collateral damage.
So, to get back to the actual question. Your group will pick its tactics based on the specifics of the situation and the public response will follow from those tactics.
If slave trade is almost entirely driven by business interest, the economic approach will work and attacks will be targeted at businesses using slave labor and the traders themselves.
If the traders are a small but influential minority, direct attacks on the people involved might be valid choice.
If slavery is seen as a political issue, attacks might aim to gain publicity and create political pressure to find a solution.
If slavery has religious or ethnic dimension, the focus might be in gaining influence among your people, not with the public.
Note that the correct choice is a value judgement the group makes based on the priorities of the people involved. So not just the circumstances of the issue, but also the people involved matter. There might be multiple groups adopting different approaches and fighting each other. The approaches groups adapt will also evolve over time.
Hope this vastly simplified and approximate answer gives some guidance on planning your group and at least makes clear that there is no single correct way.
The key point is this: The strategy follows the desired response.