bikes without panniers are very narrow and strapping long things across the back is not good for balance and does not give so many options for tying down, which is why most luggage uses 2x panniers.
if you are not carrying a pillion then strap the bag longways from your bum backwards, most bikes have a lot of room and it will give better balance and be more secure.
bags you can use could be anything, ive seen huge cricket kit bags put on securely this way, i use a 90ltr ortlieb drybag from a kayaking store.
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dave
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