I haven't gone through the process, but I work at a publishing house specialized in medical literature, and I've learned some things about drug development.

After you file your patent, I recommend you partner with a university hospital to run trials on patients. (As a routine step, the hospital's ethics committee will ask to review your study protocol to check that it complies with the Helsinki Declaration on human experimentation.)

It's very important to test your method on samples taken from patients, though you may start with lab animals divided in groups whose infection status you're blind to. With culture lines you already know what's in the Petri dish; now you need to see whether it detects the right organism when you don't know what the patient has, or whether it's actually an infection in the first place. Parameters other than speed (namely, diagnostic sensitivity and specificity) will be essential in positioning your method against the existing ones.

Edited to add: you also need those trials to find out whether there's any class of germs that your method cannot detect. I don't think you have tried with all possible pathogens.