Having moved here recently(and fairly temporarily as I can't remotely afford it long term) £500 ain't going to happen. You can get a pretty big 2 bed at 1k to the point where you might be happy sharing. Smaller 2 bed places at £750-800 but I'd think you'd feel fairly cramped sharing with someone.
There is probably cheaper but there is a LOT available in the £750-1250 range in various sizes/quality depending on area. Wolverton and nearer Bletchley have had a lot of building going on and quite a lot of flats, lots more flats around Campbell Park which itself is a really nice park to be close to.
There are parts to avoid, being in MK there are lots of quiet and nice spots and only a few you'd really want to stay away from, and pretty much anywhere in MK is quick to travel around even at rush hour.
Lots of new flats in Woburn Sands which is a nice area, bit further from central MK but still a very quick journey.
If you definitely want to live on your own on sub £600 as others have said, further out is the only way to go, Bedford, or depends where you want to live. There are some cheaper places outside of Bedford I saw when I was looking around, bungalows in smaller villages very close to Bedford.