Hi, gazzasp8,
You've got whats called an externall by-pass arrangement, this is the best way to do it, a pressure washer pump has to expell ALL the water it takes in, that's how we get high pressures, when you let go of the trigger the underloader valve traps the line pressure in the high pressure lines, as no water can flow it has to go somewhere so the underloader goes into by-pass and sends water out down the hose you have going back to bin, or if tou use a tap onto the floor.
Some machines have an internal by-pass where that hose you have goes back into the inlet to the pump, and water goes round and round instead of out. The BIG dissadvantage of the internal by-pass as the pump creates high compression it heats the small quantity of water going round and round the pump whilst in by-pass mode. This hot water gets hotter and hotter and damages pump pistons and seals very quickly (5 mins or so) very expensive to fix OUCH! So you have the best system as you can leave your pump in by-pass for a very long time possibly hours as pump will have to heat all the dust bin full of water up enough to do any damage, even on a tap the water will never get hot.
As regards the bin versus tap, ALWAYS use the bin (suction method) as there is no question of water flow IE there is water or there isn't. If your machine is 15 litres an min (15L l/m ) then it needs 15 l/m it can take this from your bin if the customers tap doesn't deliver 15 l/m then the bin will empty eventually.
Shortage of water flow will also seriously damage your pump it causes cavitation which is small explosions in the water, you can sometimes feel these as vibrations in the high pressure pipes and pump makes more noise than usuall. You won't know if your customers tap is delivering 16 l/m OR 14.5 l/m particulry when washing machine comes on, even the non return valve required by law now in garded taps reduces the flow!
Honest trust me I'm a doctor!