Extract bacteria from compost?
A first (and obvious) approach is the use of cellulose agar in order to isolate all the celluloltic bacteria in the sample. Be careful, however, since the nutrient requirements of some of those microbes may be higher and then they won't grow with only cellulose (they may need some other compounds, like a nitrogen source). Be careful with fungi, too.

If you have the proper equipment, it would be ideal to extract DNA and analyze the environmental rRNA 18s sequences. With this, you should be able to know if your bacteria is present in your sample. If so, proceed with the previous steps.

Once you had a set of suspected colonies, you must proceed with more specific culture media (wich would depend of the exact bacteria you're looking for. For example, if you're looking for Clostridium, you should try to grow your sample in an anaerobic jar and test the ability to reduce sulphur). With this approach, you may reach a point where you can't differenciate similar species. At this point, mollecular characterization is the best option, with the use of rRNA 18s again. Note that the mollecular approach, while relative expensive, can be performed in every step, so you can combine cultures and DNA analyses at will.

Lastly, if you're looking for an specific bacteria, it would be useful to know wich one is, so the community can give you more accurate responses.