Why a runner's singlet? Bike jerseys have evolved the way they have for a reason - relatively tight fitting to avoid flapping, wicking fabrics to help with comfort and cooling, long zippers in front to adjust cooling, pockets in back to carry stuff in an out of the way fashion.

When I run I wear a singlet or coolmax type t-shirt. When I bike I wear a jersey. Each has evolved in response to the needs of a particular sport. On the other hand I suppose there is nothing wrong with a singlet - it won't make you crash or anything like that.

And, if you are going to use lubricant on - ummm - sensitive tissues - use something like Body Glide rather than vaseline. Doesn't stain and make a mess like Vaseline does.