Rut, are you using the type of Bundt pan that has an intricate pattern to it?
That could prove to be difficult. I like this Nordic Ware pan.
As to the question of the skin or crust on the cake, it could be too much fat and flour.
I found that using softened butter sparingly brushed into to every micro-chasm of the pan; then the least amount of flour (of cocoa for chocolate cake recipes) and banging the heck out of it into the sink to get rid of almost all of the flour, results in the prettiest crust to the Bundt. Using too much fat and flour could be adding to the ugly outside layer on your cake, which happened to me when I used the spray and flour technique.
In addition, I use a flexible-cheap-plastic knife to release the sides of the cake as well as using a glaze to camouflage any mishaps.
*disclaimer - I am not the world’s best baker, but Bundt cakes are the one of two things I do make.