Odds of Getting In
Every business needs a bookkeeper, be it a mom-and-pop operation that needs a part-timer or a big corporation that needs rows and rows of bean counters to keep everything cracking along. There'll always be numbers to crunch.
As mentioned several times, this is not the highest paying job. To break into the field as a bookkeeper should be quite feasible, though you'll really want to sharpen your accounting skills in order to make a decent living or work for a larger company.