How much additional weight would the water have added to the bus and how much strength would be needed to lift the bus out of the water in the way that he did?
Lifting a bus full of water is one thing, as the other answers have covered in detail. However, Clark is instead pushing a submerged bus out of a lake. The fact that it's underwater actually makes it lighter due to buoyancy. Steel weighs 7.6 g/cm^3, but it's displacing water which weighs 1 g/cm^3. Assuming nearly all of the weight of the bus is from steel, Clark only has to move about 87% of the on-land weight of the bus while it's submerged. Accounting for the less-dense parts of the bus makes this figure even lower. There will be some extra weight as Clark pushes the bus out of the water, before everything drains out, but he certainly never has to lift dozens of tons of water.
Disclaimer: I know absolutely nothing about the film you're referring to. This is a purely physical answer.
According to Google, the average volume of a school bus is 960 cubic feet or about 27 cubic metres. The density of water is around 1 gram per cubic centimetre or 1 tonne per cubic metre, so the answer to your first question
how much additional weight would the water have added to the Bus
is about 27 tonnes.
As for your second question, lifting such a weight certainly requires superhuman strength. To find out just how superhuman, in terms of comparisons with other inhumanly strong characters, you may find this list interesting.
According to School Transport Online, a US "short" school bus has a kerb weight of approximately 10 tonnes.
Factoring in that the bus was around 90% filled with water and has an internal volume of around 7-10,000 gallons that's an additional 8000-9882 (US) gallons of water or around 34-37.4 tonnes of water
There are 5 passengers and a driver. There are two slender girls (weight approx 40-45 KG x 2), an adult driver (83Kg), two average weight males (50Kg x 2) and an overweight male (60Kg), that adds an additional .28 of a tonne in weight.
We can add an additional .1 of a tonne for stowage and .1 of a tonne of fuel and that comes to an approx total of