I would fall off using that method, without a doubt! I have really poor balance and can just about ride one bike, never mind two!Many years ago i loaned a mate my brothers bike (brother was not aware of this loan ) and when he had finished with it i collected on my bike. I rode with one hand on the handlebars of each which is much harder than it sounds! Just as i arrived at home feeling quite smug about not falling off i was lit up by blue flashing lights! The police wondered why somone was riding two bikes at night with no lights!
I dont think you would be able to tow a bike behind but if you can ride with one hand on each handlebar then it would be possible for short distances. Not easy though!
Why not ask the bike shop for a courtesy bike? If they have rental bikes, you might be lucky.
Why not take a friend and pay their bus fare back?
Or preferably take your granny and get her to use her bus pass.
I did wonder about this, we have an old tailgater in the garage somewhere.There is something you can fit to the back of one bike and the front of another so you can join them up. It may only work for towing kiddies bikes though.