That's why I bought the USB Guitar cable because I thought would be something I can do.
Don't worry, installing an interface would not be as complicated as this has turned out to be. The interface takes over the sound duties of the computer completely, so one driver, less latency as standard and all the controls on the front panel. The USB cable should be enough to get you working hopefully, but if not don't worry, an interface will not require all this fiddling with multiple drivers etc, and adjusting the buffer size is a standard process for setting up a little recording rig so now you are used to it you'll know what to adjust in future!
What would be another way? to upgrade my pc?
Which requirements to be able to work out the latency with Reaper?
I have what it says on the package of the cable.
Upgrading your PC MAY help, it will alow you to get the buffer size lower BUT I've had very acceptable latency on an entry level soundcard with a PC made in 2001 so it IS very doable. It would help if you let us know the specs of your PC, or at least what year you bought it, then we can see how old it actually is! 1998, gonna be a struggle, 2005, should be ok etc!
And what is the other program for? the one that came with the cable? "Guitar Rig", and "ASIO4ALL". Can neither of these help diminish the latency or the strange playback?

did I waste my money?
Guitar rig is an amp modelling program, an effects pedal for the computer, it won't change latency. You need to use Reaper to record to backing tracks, guitar rig on its own is just used to simulate playing your bass through an amp on computer speakers. Guitar rig will run as an effect in Reaper so once you have it working nicely you can use guitar rig within Reaper to change the sound of your bass. It's useful to have, but not worth worrying about till you have got it running well without!
ASIO for ALL is still worth looking at. The trouble you have is that using 2 soundcards at once (which is sort of the same as using 2 drivers at once, a driver is just a little bit of software that talks to a specific bit of hardware and allows the computer to 'use' it). The buffer is just the thinking time you allow the driver to have. A low buffer = no thinking time = need a stronger PC to get the audio through clearly. High buffer = lots of thinking time = no stress on CPU BUT latency is gonna happen.
ALL systems are a compromise between computer power and the amount of thinking time you can give it to get to a low latency. The trouble with using 2 soundcards (ie both the gtr usb cable and the computer onboard soundcard) is that it is going through the 'buffer' stage TWICE. both soundcards require a thinking time so you are effectively doubling the latency for your system. If the system was already a little weak it might be hard to get it low enough for it to work quickly when having to do twice as much work as a normal setup.
OK, thats where asio4all comes in, its a driver as well, but a 3rd party driver that specialises in helping out weaker systems by treating all the soundcards as one, hence lower latency (for those in the know, this is not quite true, but for simplicity

). So in your case asio4all may help, but as you mentioned earlier that it wasn't working when you selected it I assumed it was not going to work with your particular setup. Might be worth a bit more fiddling though.
What was the make of USB cable you bought? That will allow us to look for support specific to the cable, most have website which discuss these things and they all want people to enjoy using their stuff!
Don't worry, this is annoying but a normal stage for people getting into computer recording! I had to work all this stuff out on my own years ago, took me months but i got there! The only thing that should stop you getting a useable setup is if your computer is REALLY old, and just can't deal with the task. In which case buying an interface may be the only way to go. But post your specs. If your computer is really that old you may find just upgrading that solves everything and makes the whole recording process easier anyway.
LASTLY Smeet's suggestion will get you to a workable setup on your system straight away, and its not that hard to do. All you need is some way to split your bass signal so =
Plug bass into splitter > plug one splitter output into USB gtr cable, plug one splitter output into amp. That will allow you to play completely latency free while recording it as well. A passive guitar splitter is cheap and simple, just 1 jack 'in' and 2 jacks 'out'. You play latency free and then playback from the computer and can hear your bass recorded along to the track!