We usually prepare 30% 2ml gylcerol stocks for long term bacterial preservation at -80 degree. you can prepare 30-50% glycerol stocks for preservation of your samples.
As all the other contributors mentioned, you need to have a cryopreservant like glycerol or DMSO. 10% glycerol is sufficient but you can go higher as well. However to answer your specific question, if you do the initial freeze on dry ice you can then directly transfer to -80C. I would point out that you don't need to do the initial freeze on dry ice, when I made bacterial stocks to preserve I would add the glycerol to the appropriate concentration and just place the vial into the -80C freezer without problem. I have stocks made 30 years old that are still fine.
I agree with what everyone has said here regarding the use of cryopreservant. I would like to add that typically the dry ice flash freeze is used for strains sensitive to oxygen where you want the strains frozen right away to prevent further diffusion of oxygen. In that case it’s also often worth adding a bit of fresh medium to ensure the effective revival of that strain. I’ve never had an issue reviving strains that can survive in the presence of oxygen so I generally don’t do flash freezing on dry ice and in fact you can often streak plates directly from cryostock in that case.
I agree with the others. Glycerol or some other cryopreservative should be added before freezing to prevent large ice crystals forming and puncturing the cells from the inside. That said, transferring directly from dry ice to -80 should cause no additional problems. Any crystals that are going to form have formed by this stage.
The surface temperature of dry ice is pretty similar to -80C freezer (~ -78C), so I don't see any problem with the transfer process.
As everyone suggested, you have to make sure that the cryoprotectant has been added in your sample. Everything should be fine, unless the samples are some fastidious bacteria.