You should look into some meditation-type exercises, deep breathing, relaxation.

When I'm in that kind of situation, I generally sit down and empty my head, try not to think about bowling at all until I'm about to pick up your ball. I think part of your issue is not being able to "switch off" between shots. If you try and maintain focus all the time you're bowling, it's exhausting. The best players mentally turn off between shots, and switch back on when they need to.

Usually when I pick up my ball, my routine starts, and I'll be thinking about the line I'm playing (specifically the board my feet are on and the target board) and unless I'm doing something specifically different from my "A" game, such as lofting, changing speed, etc. that's all I'll think about, my body should take care of the rest.

It's something you can prepare for, by imagining yourself in the situation and then planting into that image, the way in which you'd like to respond, rather than the way you do (i.e. imagine yourself having the front 8, but being calm and relaxed, not thinking about the final score you might attain)
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Reporting from England

Controlled breathing. For me I start counting on my approach. 1001, 1002, 1003, 1004, 1005. This helps me keep in rhythm and focused on everything. I do it for every first pitch.

Use to when I was on the front 10 or 11 I would get nervous as usually and start my approach and feel like I had never bowled before. Awkward and out of sync. Then I started counting on my approach. Starting with my first step and 1001 ect. Made a world a difference now it is second nature and I never get out of sync or rhythm when shooting big scores. Playing sports all my life bowling was different, in that aspect of pressure until I found what worked for me.
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" men lie, women lie, numbers don't "

I look at it this way....each shot is a mere reflection of X amount of shots already done before in which I struck.  What makes this one any different??

And I went through that last night again as well as I tossed my 6th....and that's exactly what I did in the 10th, 11th and 12 shots....told myself one more just like the previous ones.

Getting the first one and then each subsequent one after makes it easier....but keeping the same rhythm as each shot before is a plus!!
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Have a drink with you to sip and if at all possible crack a few jokes with someone sitting next you to break the tension.  I have bowled 2 300's myself and been on the lanes next to someone going through exactly what you went through and I made a joke to them when I could see the color disappearing from their face.  They both came over to me afterwards and said I'm so glad you said what you said to me when you said it.  It broke the tension and I was able to relax to the extent possible given the situation.  

The other thing is remember what its like when you get there and since you have now been there you know what you have to deal with and find a way to put everything in its place.  As I say have a drink on the table and go back and relax with it and dont look at the lanes because you increase the anxiety.  When you get back to the approsch just concentrate on throwing a good shot, dont stand there longer and dont think about the situation, focus and go.

HM

Stay within yourself and remember, you don't have to do anything spectacular or different. What you've been doing is good enough, so just go do it again.

 I know this sounds over simplified, but it isn't. If you have the front eight, what you are doing is working, so just go and do it again, one frame at a time.
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Great replies, thanks heaps..
I told myself one shot at a time, tried to relax look around bowling centre, be pretty casual. But I knew deep, deep down lol, I was shi**ing myself.. I knew that I was excited as I even took my heart rate (seriosly I did), it was over 120 bpm, thats double exactly of my resting rate... I did try and follow a relaxed and carefree approach, but the emotions within myself, and the thought of is this, and the possibility of my first 300 game eventually.. I don't know, but in a weird way,it was kind of a relief when I left a single pin in the 9th, I felt like the weight of the world was off my shoulders..

Looking forward to my next 8.

This'll probably rile the old schoolers, but I take my phone/iPod mp3 player to the lanes and listen to music sometimes when my teammates conversation starts to lag. Last year for my second 300, I was feeling really good but getting a bit excited. So I threw on some of my favorite songs on the iPod, took 10 deep breaths and exhaled slowly and listened to music. It relaxed me and I didn't think about the game. Worked wonders to help me calm down.....
Other times, I've had some of my best games when a friend shows up to visit, and I'm busy chatting in back between turns and not even thinking about the game. Just goes to show you that this game is so mental at times, it's easy to over think it. Like everyone else said, do whatever you can to get your mind off your score and relax.
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Never argue with an idiot....They'll drag you down to their level and beat you with experience!