I really wanted to go when we were in Uganda but we had car troubles and so it wasn't to be. It's not the place to have anything less than a reliable vehicle! From memory it was 1.5 days hard roads to get there.
If you are not up for self driving I remember that there was a road safari advertised on the notice board at Red Chilli Back packers in Kampala which seemed pretty reasonable value considering the logistics. If you contacted them ie Red Chilli they may be able to give you contact details. I believe you can also fly in though this will I'm sure be more expensive.
As regards the security situ my understanding is it has been visitable for a year or so. I asked about it in the UWA office in Kampala back in May and they were happy to say the park was safe but fairly horrified we were thinking of driving ourselves there!