If I have placenta previa, will I have bed rest?

Not necessarily. Your OB may recommend abstinence from sex, exercise, heavy lifting and all nsaids/ssris. Bed rest has no proven benefit but is commonly recommended in cases of preterm labor, bleeding previa or both.
Not always. Previa: Placenta overlies the cervix/birth canal. Gr 1 means placenta is close, Gr 4 means it's directly overlying/blocking the baby's exit -- high chance of preterm labor & bleeding; you'd need a C/S at 36-37wks. More common in woman w/ hx of C/S & smoking. Not much you can do but wait. If dx'ed early, the uterus still grows/stretches and a placenta can migrate away even in 3rd tri. Follow w/ US.