The only one of your options which is anything like correct is the first one (exceed the limits of...). The other verbs cannot be used with this meaning. I would choose one of Charles's suggestions, or perhaps: If we change the dimensions as required, the design will go over the edges of the bed. Note that the noun 'art' is uncountable/an abstract concept, so you can't say 'an art', or 'the art' to refer to something specific or concrete. You could say 'artwork' / some artwork/ the artwork if you wish - this is also an uncountable noun but it refers to something specific. Or - as I have suggested above - you can say 'a design' or 'the design' , which is a countable noun here.

If we change the dimensions as required, it will be too big for the bed. If we change the dimensions as required, it will hang over the edges of the bed. Hope that helps.