Bulk carbonate can be OK, but only if you can be sure that you have no terrestrial carbonate input - no carbonate rocks or clastic rocks with carbonate cement in the bedrock and hinterland.
Generating robust chronology on lake sediments is really tricky. You can do radiocarbon dating on bulk samples if your sediment is organic rich but you have to remove all carbonates from the sample. If you can pull off some plant material that will also help if they are not rework. But this only goes back to 40000 years. So if your sediment core goes further than that U-Th dating is an option but you have to take lot of considerations such as Th input from other formations. 10Pb is also another common choice for dating.
On d18O stratigraphy, bulk sample is always problematic due to detrital input from surrounding carbonate formations. So if you have ostracodes and you are sure that they are not reworked, that would be a good option. Sometimes if you have snail shells in samples they might also be helpful.