Catalyzes the ADP transfer from ATP to D-glycero-beta-D-manno-heptose 1-phosphate, yielding ADP-D-glycero-beta-D-manno-heptose. Cannot use GTP, UTP, or CTP as substrate. Is not active against the alpha-anomer substrate. Is also able to catalyze the ADP transfer to beta-glucose 1-phosphate in vitro, yielding ADP-beta-glucose. ATP + D-glycero-beta-D-manno-heptose 1-phosphate + H(+) = ADP-D-glycero-beta-D-manno-heptose + diphosphate Nucleotide-sugar biosynthesis; ADP-L-glycero-beta-D-manno-heptose biosynthesis; ADP-L-glycero-beta-D-manno-heptose from D-glycero-beta-D-manno-heptose 7-phosphate: step 3/4. Bacterial outer membrane biogenesis; LPS core biosynthesis. Belongs to the cytidylyltransferase family.