Hi! I am indonesian myself. and have exactly the same story like you and your GF. I've met with my husband throught internet. Then, it was so difficult for me to get a visa, even for a tourist visa, even though I was working for respectable british company (PowerGen) in Jakarta. I was so gutted that they refused me twice, in fact my then boyfriend had to fly to Jakarta specially to complaint about this, my british boss even tried to pursued the decision, the result was zero. My then boyfriend( a.k.a my husband now) came to visit me first about twice, then I decided to come to visit him in the UK. My strong advice for you, it's better for you to come to visit Indonesia first, then you can start to think if there's a future for your relationship. I myself, wouldn't want to go to the UK first to see my then boyfriend, because you will find it is more easier for you to travelling to Indonesia than your GF travelling to the UK first.
When you find out that there is a big future for your relationship then you can go straight to the consulate (in Deutche bank building) while you are still there is the better to apply for your GF visa, It can be fiancee visa(expired for 2 years), don't have to be a tourist. But let me tell you this first, everything in the consulate is so complicated they really seems don't like mixed couple like us. Thankfully all of those done and dusted for me. I've been living here in the UK for almost 7 years, got a baby boy with my super duper loving husband and another baby on the way, great friends and great job too. I'm loving it!!!! My point is don't worry, that's right that there are some indonesian girls who wants a better living by looking for relationships with white people, but there are some genuine girls who falling in love for you just who you are, not what you've got. Good luck with your GF, hope everything smooth for you both!!!