How soon do I get my BJCP number?

Usually within two months of taking the judging exam. The local exam administrator must collect your personal information, then provide it to the appropriate exam director. The exam director validates the information and then passes it to the IT director who creates the judging records in the BJCP database. You receive notification of your new ID when this information is uploaded to the BJCP web site. The time for this process can vary, particularly with international exams. The worse case is that you get a BJCP ID assigned at the time when the exam is closed and the results reported, which usually takes two to four months.
Note that your BJCP ID is different than the certificate number you received when you took the online exam. The certificate number is not a BJCP ID; it simply allows you to register for a judging exam.