I know that i can buy a bag with straps, my question was does anybody have a preference for a good one that they have.
I wasn't particularly replying to your question, just highlighting the idiosyncrasy of adding straps to a non strapped bag as suggested by Appolonius.
regular riding: I have a small wedge bag, with elastic straps from
Decathlon for a fiver that does for an essential get me going kit - tube, spare universal cable, levers, skab patches, chain link, a couple of AA & AAA batteries, zip tie, latex gloves & small multitool inc pliers- its a bit packed in but I like to be ready for pretty much whatever regular hiccups and the wedge fits totally discretely under a roadie saddle and is lost under a more comfort orientated one. I also have a bigger and extendable, years old, Raleigh wedge bag that I can put the above kit into and personal items, rain jacket if I'm wearing regular clothes with shallow pockets that I don't feel comfortable entrusting a wallet and phone etc to.
Either are interchangeable in a matter of moments and neither leave me worrying if they're going to unclick and drop off mid ride over even the worst roads or off piste.
Daytrips: I have a dirt monkey clicky-fixy handlebar bag that is big enough for all of the above (though I usually leave the tools in the wedge under the saddle) and some food and camera etc too. its more handbag shaped than boxy so is not too odd looking carrying it off the bike too.