The rope I currently have my girlfriend says is not soft enough.
If she says it's not soft enough then she's right: as the person who wears the rope she's the authority on what feels best. The ideal solution would probably be to take her to the hardware store and let her pick out rope that feels good to her.
That said, technique matters also. Tying her a certain way may make the most of the rope you're using.
I honestly can not remember what material mine is made from but it is thicker, maybe 1/2inch or more I think. What is a good thickness and material?
1/2" is pretty thick. It's hard to tie good knots in rope that wide. Rope diameter is a trade-off: the thinner it is the easier it is to tie, but the harsher it feels. Thicker rope is usually more comfortable (all other things being equal), but it's harder to tie it securely.
For most people, rope from a hardware store is just fine. You'll do better with some more information on how rope is made. The keys are structure and material.
Most hardware store rope is made of synthetic fibers - usually nylon or polypropylene. Occasionally you'll see natural fibers, most often cotton and sometimes jute or sisal. You can get hemp bondage rope from specialty suppliers - about which more later. Synthetic fibers tend to feel slippery and look glossy. Natural fiber rope lacks that shine and feels more "nappy."
In practical terms synthetic fiber rope usually feels better. However natural fibers (especially hemp or cotton - avoid jute and sisal) tend to hold knots better. This advantage of natural fiber doesn't matter for most bondage applications: Most ties work just fine with synthetic rope. But if you want to get into Japanese bondage you might want to invest in authentic hemp.
As for structure, rope comes in three basic forms: Solid braid, twisted, and braided with a core. Braided with core is just what it sounds like: a braided sheath over a fiber core for extra strength. It's cheaper than solid braid in most cases. Braided vs twisted is pretty obvious just from looking. The difference between solid braid and braid with core is subtler: usually you'll have to check the label for that, or cut the rope - you can see the core clearly then.
I usually recommend solid braid nylon as the simplest basic bondage rope. If you already have cored rope then you can make it much softer and more supple by pulling the core out. You'll reduce the strength of the rope by about 70% but for ordinary bondage that should be fine. You just won't want to do suspension with it. But if you have a choice, go with solid braid to start.
As for diameter, that's very much a matter of taste. I usually use rope between 1/4" and 3/8". My favorite is 5/16". Some people like rope as thick as 3/8". I don't recommend rope thinner that 1/4" or thicker than 1/2".
You can get most of your rope from the hardware store. This is a good thing, since one of the firmest rules is "never buy rope that you haven't felt." The best way is to go to a hardware store that has rope on open coils. Avoid those sealed plastic packages. Look around until you find rope with the weight, suppleness, and softness you like.
There are just two exceptions to this rule that I recommend. Both are companies that specialize in bondage rope and know how it's supposed to feel.
www.rainbowrope.com sells solid-braid polypropylene in a range of diameters and every color you can imagine. If you want any color other than white then they're the go-to store.
www.twistedmonk.com sells traditional Japanese twisted hemp. If you want authentic rope for Japanese bondage, go there.
However if you don't need anything more exotic than plain white solid-braid nylon, Home Depot should have everything you need.