If One Eats Bread Without Washing Hands, Should One Recite Birkat Hamazon?

To the esteemed Rabbi, I recently began saying the morning blessings, but I do not always manage to say them in the morning. Sometimes I eat bread first and then I am unsure whether to recite Birkat Hamazon or first say the morning blessings and then Birkat Hamazon. Also, is it forbidden to say Birkat Hamazon if I did not wash my hands beforehand but still recited the blessing of Hamotzi? Of course, I try, but not always. I think I will not say Birkat Hamazon afterwards. Since I am newly observant, these things are not yet habitual for me, and I am not used to this routine. Thank you very much, honorable Rabbi.