Benedicke’s speech is written in imitation of his accent, see ‘breat’ for ‘breath’ and in the passage after that quoted in the question ‘I tinke you play the knave wid me’.
I think this allows us some latitude with the pronunciation of ‘cacke’. I propose not ‘cack’ but ‘cachou’. Per the OED a cachou is:
A sweetmeat, generally in the form of a pill, made of cashew-nut, extract of liquorice, etc., used by tobacco-smokers to sweeten the breath.
For an Italian, the 'ch' combination would be pronounced closer to a 'k' as in 'chianti', and they don't much seem to have 'cho' as a letter cluster, so the pronunciation may well be awkward for Benedicke.
Given that Benedicke poses the question immediately after commenting on the strength of ‘Jone’s’ breath, it would make sense for it to mean ‘Have you brought no breath-freshener to bed with you?’ Perhaps as a modern lover might ask ‘haven’t you brushed your teeth?’
EDIT: Revisiting this answer because I've realised that this is only half the story!
In 'Humour and Genre in Thomas Deloney’s Jack of Newbury' Jorge Figueroa Dorrego of the University of Vigo makes reference to:
Deloney’s successful use of dialogue, with colloquial language, local dialect, malapropisms and a foreigner’s broken English
It is a kind of humour which approaches satire and the picaresque and sometimes even the grotesque and scatological, generally intending to ridicule certain characters for their peculiar use of language or because they are outwitted by others
I think the broken English, malapropisms, scatology and ridicule of characters for their use of language are what we are looking at here.
Benedicke's lack of facility with English is pointed up earlier on in his tale when one of the Weavers opines that Benedicke:
should for-beare to loue, or learne to speake, or else woo such as can answer him in his language : for I tell you, that lone my kinswoman, is no taste for an Italian.
We also have an example earlier in the story of Benedicke accidentally talking shit:
First me will give you de silk for make you a frog. Second de fin camree for make you ruffles, and de turd shall be for make fin hankercher for wipe your nose. (my emphasis)
Benedicke doesn't mean to talk about crap, but his accent and command of English make it appear that he has, even though the sentence doesn't fully make sense if he was meaning to say 'turd'. And I think this is also what happens in the section the question asks about.
While @Randal'Thor's answer correctly identifies the dictionary meaning of 'cacke-a-bed', and without which I would not have arrived at this answer, I think the joke is more complex than simply having Benedicke accuse Jone of being a person who defecates in the bed. The joke is that the funny foreigner, while trying to make love to a lady (as he believes), accidentally accuses her of being a person who defecates in the bed. The meat of the humour is in the unwitting nature of the accusation.
That clearly isn't what Benedicke thinks, he is talking about her breath. If he meant to insult her in scatalogical terms on the basis of her breath he'd be more likely to ask her if she'd had her nose in shit. (Deloney doesn't shy away from shit in people's faces, in Chapter 4 the Kings Fool, Will gets a soaked bag of dog droppings flapped in his face and the association with shit and Jone’s breath is foreshadowed by the earlier turd/handkerchief malapropism). But here, Benedicke is still the hopeful lover, he wants her to sweeten her breath so that they can make sweet, sweet lurve.... So he askes her if she doesn't have a cachou handy in the bed, but it sounds as though he is accusing her of being a cacke-a-bed.
And it is worth noting that 'cack-a-bed' or 'chie-en-lit' is a noun, so even if Benedicke was suggesting that Jone had messed the sheets, he would have said 'are you a cacke-a-bed' rather than 'have you not cacke-a-bed'. The reason the grammar is 'off' is because it is correct for asking someone if they do not 'have a thing' rather than whether they 'are a thing'.