Don't you fear, the maths is actually quite easy
Right then, you want 140L for a big, deep bath. Let's say the cold mains water comes in at 10°C. FIll the bath with 40°C (actually too hot to stay in for long, but then it won't stay that warm forever either.) So, you need to provide enough heat to raise 140L by 30°C.
If your store was 140L, and you could extract all the hot water from it, then it would cool down by the same 30°C. If your store was smaller, then you'd need it hotter to make up for the shortfall in volume. The heat content is proportional to volume times temperature difference. With your estimated 100L of WBS heated volume, you'd need 30°C*(140/100) = 42°C temperature difference. Give it a little extra, and run the tank at 60°C (i.e. 50°C above incomming mains water temp). Now, extract 100L of 50°C, add 40L from 10°C cold, and enjoy.
And the WBS, if it's not a tiny one, will quite likely have a higher output to water then the solar panels. The energy content of your bath is 100L*50°C*4200J/L °C / 3600000J/kWh = 5.8kWh. If you had 6kW into water from a big stove, it'd take an hour to reheat the store.
Regarding the solar panels, I agree with the others here and recommend more tubes. 20x 58mm tubes are roughly equivalent to 30x 47mm tubes. We've got 40x 47mm into 216L, and that seems about right. Should you need it (e.g. going away during summer), then installing a heat dump is no big magic.
Klaus