Is it normal to bleed when being fingered but then not bleed when you had sex a month later?

No, bleeding is never normal - the idea that you should bleed when you have sex the first time is a myth, you should never experience bleeding when you are having sex or engaging in sexual activity. Chances are you bled when you were being fingered because your partner was rough so damaged vaginal tissues, it's normal for you not to bleed when you have sex.