You could hire someone to do the 3D rendering to make 3D objects to make the mattress. This way they already have the pricey software and skills to pull it off at a agreed upon cost.
If I was to do this, my method would be a low tech and take a 12 x 12 or larger room and mark the center of floor and then lines out from center at degree intervals for each snapshot of the mattress, and at the end of the lines a dot say 10 feet away from center allowing a 10 foot radius if travel from center all around so objects lesser than 10 feet can fit within this space and be pictured and camera remains at the same distance from the center point, and a tripod used to keep the height off the floor the same for each picture. Lighting in the room you would want to make to your liking, shadows or no shadows. I would probably go with 20 pictures at 18 degrees each snapshot if you want 360 degrees of turning ( rotation ) of the mattress clockwise/counter clockwise.
For the website to have ability for users to rotate the 3D like mattress since its actual pictures of the mattress its real and lifelike and visitors at the website could click on a left or right button web navigation buttons to turn the mattress clockwise or counter clockwise.
With 20 pictures if it starts at picture 10 and they click the right button it will step to picture #11 18 degrees counter clockwise, and if they click it again the right button its picture #12 an additional 18 degrees counter clockwise. If they keep clicking they will be able to rotate the mattress pretty quickly all the way around and end up back where they started. Clicking left button on the webpage would turn the mattress clockwise at 18 degrees per click.
You could use this room for taking anything you want to create a 3D 360 degree like view of and the HTML to pull it off would be not too complicated. Java Script or PHP etc with Java Script being the easiest to code up but primitive type of web interaction in a web world that is mostly Flash and HTML 5
If you want to have where you can zoom in and zoom out and rotate the mattress on any axis for real true 3D rendering, then the smoke and mirror type of camera trick I mentioned above wouldnt work out too well because my suggestion lost cost your on a 2D plane around the radius around the object that rests in the center of the 360 degrees. You would need a camera setup similar to Hollywood to have the camera on a track that could rotate around the mattress from any gimbal assisted angle from center point and create a spherical image request type of system possibly Numbers used for degree steps on the X axis and Letters used for degree steps on the Y axis to keep track of what image snapshot belongs where for the 4 buttons up/down/left/right to call to the correct image.
https://en.wikipedia.org/wiki/GimbalWhat direction are you looking to go... use of actual pictures to generate a 3D 360 degree like from a fixed camera angle to center environment or someone to render your mattress in a CAD like environment to make it that way?
Also do you have any experience with HTML and do you have access to your websites HTML code to alter it or do you have a webmaster who controls this?
*I took advanced photography in college as my arts program requirement and had a lot of fun with it and you really have to enjoy angles and mathematics to make seamless 360 degree panoramic where multiple pictures blend together as a loop so someone standing center to that loop of pieced together images sees it all around without transitionary flaws where each image is joined to the next. That was my final project a loop of photos taken at exact degrees out from center point, camera being center point, and the greater number of images taken the more precise the loop of spliced together pictures is without noticable flaw. Your project if a camera is used is the inverse of my final project. Instead of pictures out away from center in my project, your on the outer ring looking in to center at a fixed distance away from center point. I was going to make a hemispherical project in which someone could step in one location and lower the hemisphere over their head and look around from any angle and feel as if they are standing exactly where the images were taken but I couldnt come up with a gimbal that was without error as well as lighting was a problem lowering a hemisphere over someones head as for they are now with their head in a half circle in the dark, so a loop of images on a fixed plane spliced together was my project so that lighting for the person viewing it all wasnt a problem and looking out at a fixed axis you can see a location 360 degrees but looking up your looking at the ceiling of the classroom. I had images on a large rube like lamp shade that people could walk onto a marked box on the floor and pull a cord and this would lower the tube around them so they could look around 360 degrees from where image was taken. When they released the cord, a counterweight brought the rube with images in it back up so they could walk off without knocking their head on it or having bend down to stand up inside and bend down to walk out as well as people are different heights and so the further you pulled the cord the further down the tube traveled to where it could be pulled to anyones line of sight without havingt o look up or down at it while inside, just pull cord to desired picture height and hold the cord and look around, then release the cord and it would slowly raise back up for the next person to do the same.