Buckets are essentially a motherhood symbol in Homestuck -- the buckets we see are introduced alongside Nannasprite (2317) and Mom Lalonde’s “ironic housewife routine” (2277). This is made explicit through the trolls; the bucket represents the Mother Grub, the All Mother, to whom everyone jacks it.
More generally, any receptacle filled with a light-blue fluid seems to be correlated with the womb -- as much is suggested by the juxtaposition of Nannasprite’s life-giving blue ectoplasm with the bucket (2328). If true, this is probably connected to the running gag of girls ripping up toilets and bathtubs, but I couldn’t tell you what it means. It makes John standing in the bathtub funnier maybe? Eh. And the martini glass left for Rose (3442) would then have an association with her mother aside from the alcohol -- perhaps related to the use of ▽ as a feminine symbol.
It’s worth noting that the martini isn’t blue until Rose’s spit-take. While in Mom’s possession, the booze is colorless. And as Rose points out, Mom’s bucket doesn’t actually have any water in it (2277). I’m less sure of the martini connection, but the empty bucket strongly implies that Mom can’t bear kids -- her womb is void. This draws a connection between Roxy’s ability to summon ideas from nowhere and the mythic motif of virgin mothers, immaculate conception, etc etc. Creation from the Void.
