I know you asked for pickling beetroot recipes but this is great and easy too.
Beetroot Chutney
3lbs Beetroot
1lb Sugar
1pt Vinegar
2 Dessert spoons Cornflour
½ Dessert spoon of Gelatine
Wash, peel and grate beetroot.
Put vinegar & sugar in a pan and bring to the boil.
Add beetroot & cook for 5 minutes.
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Dissolve the gelatine in a little vinegar.
Mix the Cornflour with a little vinegar.
Add them both to the beetroot.
Cook till thickened.
Put into jars.