This paper reports on the development of a technology involving $^{100}$Mo-enriched scintillating bolometers, compatible with the goals of CUPID, a proposed next-generation bolometric experiment to search for neutrinoless double-beta decay. Large mass ($sim$1~kg), high optical quality, radiopure $^{100}$Mo-containing zinc and lithium molybdate crystals have been produced and used to develop high performance single detector modules based on 0.2--0.4~kg scintillating bolometers. In particular, the energy resolution of the lithium molybdate detectors near the $Q$-value of the double-beta transition of $^{100}$Mo (3034~keV) is 4--6~keV FWHM. The rejection of the $alpha$-induced dominant background above 2.6~MeV is better than 8$sigma$. Less than 10~$mu$Bq/kg activity of $^{232}$Th ($^{228}$Th) and $^{226}$Ra in the crystals is ensured by boule recrystallization. The potential of $^{100}$Mo-enriched scintillating bolometers to perform high sensitivity double-beta decay searches has been demonstrated with only 10~kg$times$d exposure: the two neutrino double-beta decay half-life of $^{100}$Mo has been measured with the up-to-date highest accuracy as $T_{1/2}$ = [6.90 $pm$ 0.15(stat.) $pm$ 0.37(syst.)] $times$ 10$^{18}$~yr. Both crystallization and detector technologies favor lithium molybdate, which has been selected for the ongoing construction of the CUPID-0/Mo demonstrator, containing several kg of $^{100}$Mo.
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