To be explicit, an ordinary bubble level won't cut the mustard. They're good for putting up shelves and most other purposes but aren't sensitive enough to detect a twisted lathe bed.
You need an Engineers aka Machine Level. They are made to detect tiny deviations from level, as required to set a lathe accurate to a thou or two over several inches. Typically, in a new installation the lathe stand is set up with an ordinary level first, and then the lathe is tested. If not cutting straight a Machine level is used to check for bed twist, which can be corrected by shimming a foot: some machines have screw-adjustable feet.
This example is made by Dasqua and sold by RDG.
In theory new lathes are confirmed to cut straight on a true level surface in the factory, so plonking them down on any decently stiff flat surface should be good enough. In practice, don't expect too much of inexpensive hobby or elderly lathes. Note flat rather than level. It's not necessary for lathes to be level provided the bed is straight: they work perfectly well in storm tossed ships. Levelling is just one way of eliminating twist, and a bent stand is one way of accidentally twisting a machine.
In my book Machine Levels aren't good value for money. Pricey and much too sensitive for ordinary work. Fussy and the bubble takes an age to settle. Good for anyone installing lots of machines, dubious for putting one into a shed! After being used once to set-up the owners lathe, I suspect most Machine Levels end up in a cupboard. As an alternative, Rollie's Dad's Method takes longer and is more complicated to do than detwisting with a good level, but it requires no special equipment.
A word of warning: high-precision measuring is so difficult it's quite easy to lead oneself up the garden path into a deep maze of confusion. A wobbly DTI moving on a slide will cause trouble. When measuring into the 0.02mm / 0.001" region don't rush to adjust anything based on amateur measurements: they're likely to be flawed because taking them properly is a skill you don't have!!! Therefore, keep measuring simple and use the right tools: detect taper with a micrometer, not a DTI. Check everything – it may take several hours practice to get a micrometer to repeatedly read the diameter of a precision rod consistently. Positioning the micrometer correctly is important, and so it applying the same pressure to the screw every time. The ratchet helps, but trained craftsmen rarely use it; they develop a 'feel'. Some are better than others, so find out how good you are by practising. In the meantime, don't jump to conclusions!
Dave