The problem with transporting your own reaction mass is diminishing returns.
In other words lets say you have a space ship that weighs 0.5 tonnes, and you carry a tonne of fuel. This will let you accelerate to X m/s.
Now if you want to accelerate to 2X then you need to accelerate twice as much, so take twice as much fuel, right?
Unfortunately not, because you also need to accelerate all the fuel.
So in the first example the average weight of your ship over the duration of the flight was 1 tonne.
In the second example if you double the amount of fuel the average weight is 1.5 tonnes. You do go further than X - but you go 2/1.5 which is 1.333. In other words you double the amount of fuel and actually only gain 33% more final acceleration.
This is a massive over-simplification, and things like the ratio of fuel-mass to ship-mass make a big difference. It does show you though that it gets harder and harder to just add more fuel.
This is why things like the EM Drive are such a big deal. If it works you don't need to carry reaction mass, and that is huge.
You can work around this a little using things like a Hohmann transfer orbit and being content to spend a lot longer travelling at a lower speed rather than constantly accelerating, it's all tricky though and there is no straightforward solution.