When is it safe to put my baby in a bike seat or a bike trailer?

Depends. Once baby has reliable strong head control, usually by 6 months, either should be safe. Children in bike seats should wear a helmet. Look for a five-point restraint system and less-traveled roads with bike paths.
About 6-9 Months. Going for a bike ride with mom or dad can be a lot of fun for you baby, but you want to make sure they are safe. Infants should not ride in bike seats. What if you crash? They are going down too. Bike trailers with flexible hitches that allow the bike to fall but keep the trailer upright are your best best. Good head, neck and trunk control are essential for the infant. Helmet too!
Good Head control. Good head control is something that you want your child to have before you put him in a front bike carrier(it is attached in front of you). For a bike trailor (that goes behind the bike) you might do it a little bit earlier as they are reclined but there may be bumps on the road that he might not be able to handle very well.