Wendy
That is very common.
Check with your bucket again the flow from the hot and cold bath taps. It will be unusual if they are both the same. If you feel the pipes, I think you will find the 22mm pipe is hot from the cylinder, and the 15mm is cold from the main.
Isabeller
if you have a combi, you can't have a power shower. A power shower sucks water out of a cylinder that is supplied from a loft tank and pressurises it. (However if you have both a combi and a tank, you can. This is uncommon but can be useful especially in larger houses.)
You can have an electric shower (though it will be very weedy, especially in winter) which you can also use when your combi breaks down.
However with no loft tank, the amount of water that comes out of your electric shower, added to the amount of water that comes out of your combi, added to the amount of water that comes out of your cold tap, WC cistern or washing machine, at any one time, will be limited by the amount that the incoming water main delivers, so turning one on will reduce the flow from the others.
If you are lucky enough to have a large incoming water main that delivers, say, 30 litres per minute, then you will have plenty to go round. If you have a small flow of 12 litres per minute, that will be very poor when shared between two or more taps.
You can use solar to heat a cylinder, but the source of heat is irrelevant to the amount of water flow.