I'd do this, and run 2 cables while you're at it for redundancy as it'll be a lot cheaper than digging up your garden again if it breaks. Also allows you to physically segregate traffic e.g for CCTV.Personally, dig in a duct and put fibre and/or cat5e or higher in it. Then run a switch in the studio, along with its own AP.
This is the best way.When you dig in the armoured cable for the power, dig in some BT duct 56 next to it. Rope external grade Cat6 through here and then since it's a duct you can pull fibre through in future.
Do not bury stuff like flexible 25mm conduit, it's a pig to try and pull things down later because it's ribbed and 25mm OD conduit is not really big enough to pull cables through over any decent distance.