Looking at how these apparently mainly German and Dutch operator restraints are described, discussed or referred to in English (side restraints more often than not, in line with the valid comments made at the outset by Armorel), turning it around in this way might be an option, especially if you would like to keep the reference to door in the actual name rather than using something longer and descriptive like "side restraints that operate like doors". I do think that bar is the most appropriate translation for Bügel here.

A few references (in no particular order):

Another much discussed trend was the addition of side restraints. Imagine a counterbalanced sit-down rider with bars mounted on the side of the compartment that the operator swings open like a door to get aboard. With this feature, if the lift truck tips over, it acts as a cage to keep the operator in the vehicle. Although these are not standard features on any U.S. lift truck, Wood says he’s seeing more and more special requests that could eventually become standardized.
http://mhlnews.com/powered-vehicles/drive-your-lift-trucks-d...

SAFE OPERATION WITH FORK LIFT TRUCKS
Wear a seat belt, or if not fitted ensure that the cab doors are closed or side restraints are in position.
http://eiga.web1.apollo-com.be/fileadmin/docs_pubs/Doc_165_1...

A German-manufactured forklift driver restraint, BodyGuard, is now available in Australia and New Zealand.
The restraint is a foam-padded door bar made of plastic and metal that does not protrude beyond a forklift’s outer contours.
http://www.forkliftaction.com/news/Forklift-safety-attachmen...

We have heard endless debates in operations about whether it is needed to buckle up if the forklift has an enclosed cab and or door bars.
http://www.buildsafe.co.za/Files/RFI 039 - ANSWERS.pdf
[Apologies - I can no longer get this link to work]

The term is also turned around in German:

Die wohl sinnvollere Lösung ist die Verwendung von Tür- oder Sitzbügeln. Diese werden z. B. am Rahmen des Fahrerschutzdaches oder hinter dem Fahrersitz montiert und können wie eine Tür geöffnet und geschlossen werden. Sie verhindern, dass der Fahrer beim Kippen seitlich herausgeschleudert wird oder das Fahrzeug in Panik verlässt (Bild 2-7).
Bild 2-7: Bügeltüren als Rückhalteeinrichtung
http://www.bgbau-medien.de/zh/z92/3.htm

Eine Alternative ist das Türbügelsystem. Seitlich am Fahrerplatz angebrachte, umschäumte Bügel lassen sich wie Türen schließen und sorgen bei einem Kippunfall für ausreichenden Freiraum zwischen Boden und Stapler. Toyota bietet beispielsweise den Lifesaver an. Das einbaufertige System kann einfach montiert werden, ohne die Außenkontur des Fahrzeugs zu überschreiten. Ab sofort ist auch eine neu entwickelte Bügeltür von Linde erhältlich. Dank eines Dachadapters eignet sie sich zum Nachrüsten aller Stapler-Baureihen.
http://www.industrieanzeiger.de/home/-/article/32571342/3426...

You could also look at the English-language material of some of the Dutch and German manufacturers and perhaps even contact their UK offices for information.

Eblo
http://www.eblosafety.com/wordpress/wp-content/uploads/EBLO_...

Still
retaining bar doors http://www.locators.co.uk/res/RX50 Technical specification.p... or restraint system with bar doors http://www.northernforklift.co.uk/pdf/r70diesel.pdf

BTW - A vaguely similar concept in English can be found in relation to 4x4 vehicles – bar doors, tube doors, custom roll bar doors, etc.
http://www.fourwheeler.com/features/0708-4wd-1997-jeep-tj/ph...
https://flint.craigslist.org/cto/5377545931.html
Try an image search for “bar doors” [or “tube doors”] + “4x4” [ or “jeep”], e.g.
https://www.google.co.uk/search?complete=0&biw=1280&bih=861&...