ride with (one)
1. To travel together with one while riding on a vehicle or animal. A noun or pronoun can be used between "ride" and "with" to specify what is being ridden. I love riding bikes with my kids. Why don't you take your pony and ride with me out to the edge of the farm.
2. To accompany one inside of a vehicle as a passenger. Do you want to drive with us or with your friends when we go out for dinner later? I rode with the ski team on the bus, even though I wasn't competing that weekend.
ride with someone
to travel with someone on or in a vehicle or a beast of burden. I'm going to the store for some milk. Do you want to ride with me? Can I ride with you to the store?