They both have a lot of calcium but the uses are different

Lime is used mostly to raise the pH of soil, though it also adds calcium. Use lime if you need to raise garden soil pH, a soil test will tell you this. But if you are using potting soil you do no need to add lime.

Bone meal contains some nitrogen and a lot of phosphorous as well as calcium. Phosphorous builds up the root system of tomatoes, bone meal has it but lime does not. Mix it into the soil well, don't just sprinkle it on top. The calcium helps against blossom end rot; however you probably need some other source of additional nitrogen and also potassium, because bone meal just by itself is not a balanced fertilizer.

I'm trying Lobster Compost which has plenty of calcium to prevent BER. I'll let you know how it goes end of season.

Since you are growing them in containers you need a balanced low-dose fertilizer that provides all three N-P-K nutrients as well as some micronutrients. Neither lime nor bone meal does that so I would suggest you pass on both of them for container growing. Neither is fast acting so neither would correct your problem for the current season.

There are many well-balanced fertilizers made, both low-dose organic and chem based, and several made especially for container growing. The link below discusses several of them or consider one of the Epsoma ferts, fish oil emulsion, time-release soil additives, or regular use of compost tea.

There are many causes/contributing factors to BER and calcium management is only one of them. This is especially true in containers. Unstable weather (as you mention), inconsistent watering, excessive use of nitrogen (determinate growing like indeterminates might be a sign of that), root bound plants, container size, top growth exceeding root support, poorly draining container mix or excessive draining that cause washout of fertilizer, etc. It is difficult but not impossible to avoid them all. ;) Good luck.

Here is a link that might be useful: Fertilizing Container Plants

if you put the meal on the bottum of the hole you dig buy the time the plant starts to flower it will be ready to be used by the plant