None of the parts are a problem; you can even buy flexible panels of RGB programmable LEDS:
For advanced NeoPixel fans, we how have a bendable, flexible 8x32 NeoPixel LED Matrix! Control all 256 ultra-bright LEDs using a single microcontroller pin, set each LED as you wish to ...
That is actually rated at 77 Watts at full brightness, so a fraction over 15A at 5V. At low brightness it would take rather less power.
A small MCU such as an Arduino or PIC to control them, plus something like an HC05 bluetooth module to communicate with it, and a big 5V buck converter.
And one of the many "moving message" programs such as this:
2014/03/16 Update: The source code to this is now on GitHub. Check the Arduino link at the top of each page of this site. Yesterday evening, I coded up a simple scrolling message sign that use…
As Pommie says, the big problem is the amount of power needed. Even something like a big electric drill battery pack or RC flight pack, 18/20V 5AH would only run it for an hour or two with that type of power consumption.
Using conventional LEDs with a matrix drive would be far more power-efficient, though at the cost of it being a single-colour display.
You could use some MAX7219 LED drivers plus normal LEDs to duplicate something like these, but on a curved base, rather than the moulded LED modules; using high brightness LEDs that could be made very power efficient:
A single module can drive a 8x8 dot matrix common cathode. The left side of the module to the input port, the right to an output port. Module with input and output interfaces, support for cascading multiple modules.
www.ebay.co.uk
Each IC (or ready made PCB module) will drive an 8x8 array of LEDs:
Find many great new & used options and get the best deals for MAX7219 Dot led matrix MCU control LED Display module for Arduino Raspberry at the best online prices at eBay! Free delivery for many products!
www.ebay.co.uk
And this is a bluetooth-linked moving message display project using those MAX7219-controlled LED arrays:
Making a Moving, Wirelessly Controlled LED Display: Introduction I have used LED matrix displays for a number of different projects over the last few years. These 8x8 LED units have a controller that allows an Arduino to talk to them sending text or graphic information that can...
Or several small LCD panels would also work; eg. the common 1.44" 128x128 pixel ones take less power than a single Neopixel type LED.