Detection is a big problem with Bio weapons because of the incubation period. It may take several days or weeks for the victim to become sick and depending of the bio agents, some of the early syndromes can be similar to common disease such as flu. In this case, wrong early diagnostic can delay the detection time and be life threatening for the victims (because when the right diagnostic is made the patient often is in an advanced state). There is 2 scenarios: either the release of bio weapons has been detected via specialized detectors or the detection happen when it's already too late (post contamination detection, at the hospital for instance).

I don't want to go into sensitive details but there isn't much full time bio-screening system all over the world that would monitor the air 27/7 in a subway for instance. The military uses early warning detectors when they stack troops or resources in a sensitive area but in the vast majority of the situation, a stealthy bio-terrorist attack will be unnoticed until many people start flooding the hospitals with exotic syndromes (at this points, CDC in the US would be alerted for instance). Also, bio-detection and identification is a very complicated business. You need several steps (early warning, ID), expensive devices and costly consumables. There is also a lot of false alarm which is why constant screening is complicated (can you close a subway each time a detectors goes off?)

So after detection and identification there are two main questions: 1. Is the agent contagious ? (eg anthrax is not) 2. Is the agent contagious during the incubation period ? (people are sick without knowing it but can contaminate other people)

Vaccination isn't an option for the victims because vaccines only work if administered before the contamination. At this point the first responders and health care professionals with reinforcement from specialized units will work on isolating the victims and finding the source of contamination to trace back all the potential persons involved in the original incident and stopping them from traveling and contaminate other people (assuming the bio agent is contagious, which is not always the case, eg anthrax). If the crisis becomes out of controls, such as smallpox outbreak the authorities can start mass campaign vaccinations (only Japan an US have enough stockpile of vaccines, and there is no guarantee they would work on a special strain) and take other specific containment measures. It's very hard to say what a realistic time frame is because it depends of many factors (type of agent, contagious or not, contagious during the incubation period, location of the original release, etc) but time is a key element.