Firstly, a specific response against the attacking antibiotic. These can take the form of antibiotic degrading-enzymes, or efflux pumps, which move the antibiotic out of the cell. In the case of bacitracin, it's an efflux pump (encoded by the bcrABC cassette), which uses energy from ATP to transport the bacitracin out of the cell.
The most interesting thing about this system, and indeed many of the antibiotic-specific response systems, lies in it's evolutionary origins. The cassette originally came from a bacteria called Bacillus licheriformis, which is the bacteria that makes the bacitracin antibiotic in the first place. Soil bacteria tend to make a huge number of antibiotics, for defense and invasion, and if you make an antibiotic, it's a good idea to have some way of ensuring that it doesn't destroy your own cellular systems. In fact, given that this is an efflux pump, it might not even have evolved as a defense mechanism...just a pathway for moving the bacitracin into the environment once it had been made, as it is a secreted antibiotic
These ABC transporter systems are found fairly frequently as well. In B. subtilis (one of the better studied bacillus bacteria) eight out of the forty antibiotic genes have ABC transporter systems next to them. Because unlike in eukaryotes (like people) who can often have genes for similar systems on wildly different parts of the chromosome, bacteria like to keep genes used for the similar functions close together. They don't have much genome, they don't have the space pr the protection of a nuclear cell membrane, so they have to be more efficient about packaging.
The second type of response is a more generalised system; rather than responding to a particular antibiotic, it is instead a cellular response to the damaged cell wall. As an example the LiaRS system (a two-component response system)is activated in response to four different cell wall attacking antibiotics (all of which interfere with the rate limiting step of cell-wall building, the lipid II cycle). The Sensor (LiaS) has a short histadine kinase domain which is buried in the membrane. This recognises membrane damage and uses the energy from ATP to phosphorylate the Response Regulator (LiaR) which then leads to gene activation.
The Lia system is more than just a two component system however, there is a third component. As well as the sensor and responder, there is a third protein LiaF which keeps the system 'switched off' when the cell wall is not damaged. This is shown diagrammatically below:
Image from second reference (Jordan et al 2006)
When the cell wall is damaged, the LiaF inhibition is removed, and the LiaS can phosphorylate the LiaR, leading to a change in gene expression, which produces the appropriate response.
Unlike the specific responses, these pathways are often present within the bacteria, as a natural response to cell wall damage. These are not so much resistance mechanisms, as survival mechanisms, that are strongly selected for in times of antibiotic stress. The damage caused by clinical concentrations of antibiotic is usually too much for such systems to cope with, but they form an adequate defense against antibiotic levels in the soil.
Ohki, R., Tateno, K., Okada, Y., Okajima, H., Asai, K., Sadaie, Y., Murata, M., & Aiso, T. (2003). A Bacitracin-Resistant Bacillus subtilis Gene Encodes a Homologue of the Membrane-Spanning Subunit of the Bacillus licheniformis ABC Transporter Journal of Bacteriology, 185 (1), 51-59 DOI: 10.1128/JB.185.1.51-59.2003
Jordan, S., Junker, A., Helmann, J., & Mascher, T. (2006). Regulation of LiaRS-Dependent Gene Expression in Bacillus subtilis: Identification of Inhibitor Proteins, Regulator Binding Sites, and Target Genes of a Conserved Cell Envelope Stress-Sensing Two-Component System Journal of Bacteriology, 188 (14), 5153-5166 DOI: 10.1128/JB.00310-06