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The LVT flooring can take the weight that's not a problem. A floating floor needs to be able to contract and expand and ideally cut to within a quarter of and inch to the tub then trimmed out. In a room as small as a bath it's not as critical though as long as the flooring is not cut tight to the walls. It will look cleaner without trim so go for it. The trim I use for tubs and showers is a low, pliable vinyl product with a flared toe. I buy it at my flooring supply house but I'm sure you can find it on line or maybe at home depot. I only use the stuff when necessary like when a tub is shimmed for level.
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