Hello,
I have heard that it is possible to obtain a Chinese Visa from Bishkek in Krygyzstan. I've also read about a company called Celestial Mountains that can assist with this, (in particular the crossing via the Torugart Pass). Has anybody out there had any experience of this?

I don't have experience of applying for a Chinese visa in Bishkek, but reports from other travellers indicate that you should use an agency in Bishkek to assist you if you can afford to pay a fee for the service. Here are some threads to check:
Torugart crossing Kyrgystan-China around 27/28 sept 2010
China visa?
However, I have used The Celestial Mountains Tour Company to travel from KG to CN.
In August 2009 I contacted a fellow TT poster who had advertised for a travel partner to join her for the crossing. She had already started organising the trip with Celestial Mountains, which charged us USD 400 for two people to travel from Naryn to Kashgar. We organised all the details by email beforehand, sending scans of our passports and visas. When I got to Bishkek I picked up the necessary paperwork from the CM office and paid the first USD 200. I made my own way to Naryn to meet the TT poster for an early morning departure on the travel day. She paid the remaining USD 200 to the Uighur driver who met us at the border.
The CM staff in Bishkek are charming and efficient, and the driver who met us in Naryn to take us to the border spoke no English but was friendly and agreed to stop for photo opportunities when we asked. Which was often. He waited with us at the border until it opened after the Chinese lunch break. Overall, the journey was relatively comfortable and stress-free.
Here's the CM web page with information on the Torugart crossing (it looks like no one has updated it for a long time):
http://celestial.com.kg/articles/travel/Border-crossing/Torugart-FAQ-(Frequently-Asked-Questions)_220.htm
If you decide to use CM for visa support, it probably makes sense to use the same company for the Torugart crossing. However, reports suggest these companies may arrange the crossing more cheaply:
Community Based Tourism: http://www.cbtkyrgyzstan.kg/
NoviNomad Company (the page on Torugart): http://www.novinomad.com/seite.mv?57-10-00-00<i>&uid=4CDD03A8000D22330000739100000000</i>&lg=en
At the first Kyrgyz military checkpoint as you approach the border region (it has barbed wire and watchtowers, but you're still a long distance from the border itself), the guards will check your passports and the driver's authority to enter that area. There is/was a middle-aged guard posted there who collects coins, so don't worry if he asks you for money. He is very friendly, and life in that remote area is quite dull.
Be carefull, the last people I met applyıng for Chınese vısa ın Bıshkek AND Dushanbe got ıt refused ! The best place to get ıt ıs Tashkent. It's fast (1 day) but expensıve (100 dollars).
I met a swıss guy who got ıt ın bıshkek, but the same day on french guy dıdn't get ıt and some other people had a very long waıtıng tıme !!!
So try Tashkent I suggest !

We (2 UK passports) got a Chinese visa in one day in Tashkent last week. Arrived 10.30AM no queue. Filled in forms, fotos, copy of passport, passport and $100 each and collected 5PM Really easy.

I got my chinese visa in Bishkek today. It took 4 days and I had to go through an agency (Kyrgyz concept). Also it was quite expensive (150 Dollar), but still cheaper than travelling to Tashkent. ;)

We (US and Irish passports, never previously been to China) obtained our tourist visas for China in Bishkek also using Kyrgyz Concept. Their price was 250 USD for US citizens and 100 USD for all other nationalities. This included the consular fees. Add 50 USD for same/next day service. We showed up at their office on a Thursday afternoon, handed over our passports and paid their fees by credit card. They took our pictures and asked us to write down our home address and professions. We returned to their office on Friday afternoon and retrieved our passports with the visas inside. No applications to fill out, no need for us to go to the embassy. Easy, but pricey.
They (KC) told us it would be difficult to obtain 60 or 90 days in Bishkek and were only able to get 30 days. Extending in China was easy (Xichang, Sichuan - same day), but very expensive for US citizens.
They (KC) also told us that the consular officials sometimes ask to interviews the applicant, but that this usually only happens to French applicants.
We met other travellers in Bishkek who used other travel agents to get their tourist visas for China for slightly less money. We also met travellers who obtained 90 day tourist visas in Tashkent with no hassle.
Finally, it's probably worth noting that before Bishkek we were denied by the Chinese embassies in Vienna, Bratislava, Budapest, Belgrade and Istanbul because we we weren't residents of the countries they are capitals of.