Hi Wildy, I take it you want to inflate an airtight bag with air, not a gas (helium), so the device to do the inflating would need to be a small battery type pump, like the small hand held portable battery powered tyre pumps you can get for when your car gets a soft tyre and you can't manage a foot pump etc.
The type of rechargeable electric porta pump I have seen is available on the 'net and various auto shops that do gadgets for most anything car wise.....I don't think camping type air bed inflators would give you enough pressure or flow rate, but they do get an air bed to be pretty firm, so they might work.
Not having seen your design for a bag lift, I am guessing that it's going to end up like a square (round?) box (but an inflated bag in that shape), sized about 16" X 18" and 18" in height so that you can sit on it and elevate yourself to that height.
Anything you pressurise will want to assume a sperical shape in all directions unless restrained in those quarters.
So, if'n you start off with a round tubular shape, say 16" diam, made from some rubberized canvas material, 'cos it's flexible and tough, you could probably have a shape that looks like a flat doughnut, but gets to be a fat doughnut when it's inflated.....they have something like this for jacking cars up, but using the exhaust pressure from the engine to do the lifting, and it will lift the side of a car to enable you to remove a wheel etc.
The pressure for lifting is proportional to the weight lifted, so the larger the surface area the more you can lift or the less pressure you will need.
To achieve a tubular shape (concertina?) you would need to restrain the diam by doubling with bands of material so that the shape remains a tube as it gets longer with pressure.
You could get an old air mattress and cut it open to see how it holds it's shape, and resew it up to achieve your design.
I would think that a square shape would need internal restraint corner to corner to prevent the overall shape from bulging sideways into a round ball shape, so a round shape might be better.
I would also think that if'n you had the internal tube divided into 3 or 4 chambers stacked on top of each other, attached to each other, and interconnected to each other, and inflated to maintain a shape, you would have better control, especially when the load is removed at the end of the lift.
Gluing the material is not a recomendation, but I would start off by looking at a rubberized canvas material (awnings, air beds, garden pools?) that you could machine sow together and still have enough air tightness to enable the bag to inflate, and a control valve to hold the pressure, but enable you to release it progressively.
You might want to consider the top surface to be a shape that would enable you to not slip off sideways, (catastriphically), so it would probably have a depressed shape to fit your bottom end.
One ballon like bag will go out of control as soon as you shift your weight on it, so I envisage a number of "pancake shaped" seperate interconnected internal chambers as being necessary.
Hope this helps you...we're full of ideas on here....you might want to go into business if'n you get the design right.
BTW, you could also get some used and discarded air bags from auto wreckers to play around with....might give you some ideas and cheap material to work with.