You can buy new sickbeds at the Architect's in Fractureford for 150 hD per bed.
To take the bus to Fractureford, click on the bus stop and buy a ticket on the left-hand side menu. You can see how many tickets you currently have on the top left-hand side. Click the map on the right-hand side to use one of your tickets.
Once validated, a ticket is always valid until the end of the day. You are given 3 free tickets at the start of the game, but you will have to purchase any further tickets yourself. On Wednesdays and Saturdays you can travel to Fractureford free of charge, by the way!
If you have a valid Premium Account, you can also purchase a flashy car at the car-dealer in Fractureford, allowing you to travel there without needing to take the bus at any time.