At the minute I've got no spare time whatsoever
I'd argue that it's more time consuming taking the bike to the LBS than it is doing a quick adjustment at home.
At first, it takes up a fair bit of time. Reading instructions, watching vids etc.
But once you've done a particular job once, the next time will be easier. You'll know what to do, how to do it, which tools to get out of the toolbox.
You'll also get good at "on the road" diagnosis. If your chain "clunks" down as it moves to a smaller ring on the cassette, you'll be able to make a quick adjustment in seconds and put it right. If your disc brakes bind, a multi tool and maybe one minute of your time will sort it.
You'll also get to know how long consumable parts last (disc pads, chains, cassettes, chainrings etc.). You can then buy those parts in advance ready to fit when needed. If you buy parts in off peak periods (middle of winter), you can save some serious money.
The risk with set period servicing is that you will be either paying for parts to be replaced which still have months of use left in them, or you will be paying to have damage repaired caused by a failure to replace a part when needed (the chain is the classic example).
You could start by learning just one job. Maybe indexing would be a good start? Gears are designed to be user adjustable and the job requires minimal tools. You don't have to do any "stripping down and putting back together" either. Well indexed gears last a lot longer than poorly indexed gears which is another time and money saver.
Give it a go.