Lee,
You will need to use the correct type of paint for the underlying material, particularly if the material is flexible or has special properties.
GRP - visit a yacht chandler or a GRP repair specialist - they sell a range of GRP paints and thinners.
Something like "International Top-Lac" is available in a range of colours and is designed for repainting GRP boat hulls (above the water line). And if it lasts on a boat, a caravan is easy in comparison.
Bumper - if this is GRP - use the same paint.
Bumper - if this is Acrylic capped ABS - then the same paint may be OK but seek advice from a specialist paint shop. Acrylic capped ABS is used for car bumpers and the inherent flexibility makes it difficult for normal paints to stick.
How to tell:
The backside of GRP is usually rough with obvious bits of glass mat - unless the GRP moulding is double skinned when the backside will be smooth too.
The backside of Acrylic capped ABS is smooth.
Robert