It looks like you will have to run a new wire to feed the shop. You should consider running a wire big enough to provide at least 60 amps of current at 240 Volts. The cost of the wire is small compared to the installation cost. This will give you power for future growth, considering lighting, multiple 120V circuits, a little heating, and more machines.
Wire for wet locations has a "W" in the designation code. This does not apply to direct-bury wire, which has it's own codes.
Buried PVC conduit allows you to use regular (rated for wet location) wire, instead of direct-bury wire, and the cost is somewhat offset by the added protection the wire gets from the conduit. The conduit also allows the wire to be replaced without further digging, and running an extra conduit gives room for future expansion with little added cost. It is wise to run a 1" or so conduit in parallel on the far side of the trench for data/communication use now or in the future. In the big scheme of things, PVC conduit is inexpensive, and can save you a lot of money in the future.