Let me just say, I'm a new Yogi. Always enjoyed it, I would take the classes offered at my gym, I would buy videos, etc, but I was never hardcore about it. I recently, however, joined a bikram yoga studio, and love it. It is a challenge, but once you get acclimated to the heat, I think you'll be okay, I think thats the hardest part. Be ready to sweat though! Drink lots of water throughout the day. If you feel at all dizzy, just sit down, breathe, focus. You'll feel better.
As far as safety, I think as long as you listen to your body and stop when it tells you to, you'll be fine.
I try to wear as little as possible, shorts and a sports bra, but there are people who wear pants, its up to you. Bring a towel for your mat and water. Go with a clear mind. Im not going to lie, there are days where some poses are harder than others, every class is different, but I always feel good when Im done.
My advice is find a studio, see what introductory offers they have, and try it. The fact that you already do yoga helps. If its not for you dont feel bad.
Good Luck! Namaste.

DON'T DO IT!!!
That's the best advice I can give. Its dangerous and unpleasant not only in terms of how smelly the room is, but more importantly in how you feel during and afterwards. If you been doing ashtanga for years then you will be disappointed in the lack of a "workout" that you get from bikram. You'll sure sweat, but the sweat isn't honest, it doesn't come from challenging your muscles, it just comes from being in a room that smells like feet (and MUCH worse!).
I am a daily vinyasa practioner and teacher and I'm pretty flexible, but I'm only flexible when my muscles are properly warmed up, and muscles warm from the inside out. Meaning, you have to increase your heart rate by doing actual physcial activity to get more blood flowing to your muscles in order to begin to stretch them, they won't just "become more flexible" because you are standing in a dangerously heated room as bikram posits. In fact, I left the one bikram class I've taken with a pulled muscle because I wasn't properly warmed up enough before streching, not to mention feeling utterly dehydrated and annoyed that I wasted 90 minutes that I could have actually done something good for my body and exercised instead of standing around in an glorfied sauna.

I think different practices work for different bodies. My dosha is pretty dominant kapha so I wanted something to bring out more fire/pitta so this is my first week doing Bikram, and I love it. It is definitely a workout. I had a positive soreness in my muscles after the first class. It really worked my back and sides and after just 2 classes I feel that my posture is better. I agree with Caldarete, you body feels different in the postures from day to day and if it's not for you, it's not for you.

I love Bikram! You should definitely try it. Like Caldarete said, you should wear shorts and a sports bra, or if you don't feel comfortable in that, a tank top is fine. The people who go often have special hot yoga shorts, but that's not necessary. Drink LOTS of water before you go, and it will make a huge difference in terms of how you feel. Every once in awhile, I'll still have an off day where I have to sit out some asanas, but it's totally fine and nothing to be embarrassed about. Bikram instructors are very big on listening to your body and being honest with yourself, and they will encourage you (and everyone else) to stand or lay down if the heat is getting to you or if you just feel tired. Otherwise, it is a GREAT workout and it will definitely get your heart rate up if you do everything correctly.

When my schedule is busy and I take some time off from Bikram, my first class back is always tough, but then I get used to it and start to feel AMAZING after class. I cannot say enough good things about this type of yoga. If you do it correctly (i.e. listen to yourself and push yourself to where you're getting a workout but not beyond your ability) you will see and feel amazing health benefits. For one thing, it healed a running injury that I had for an entire year. My skin looks better, I have more energy, and it's great for losing weight. If you can't tell, I'm quite a fan

I'm going to try the Bikram beginners class on Monday... wish me luck!