The silver palate cookbook has an excellent carrot cake recipe; it uses cooked, pureed carrots instead of grated/shredded carrots. We have won awards and first place finishes in competitions with this recipe. You can leave out the nuts (there's no raisins/sultanas, those don't belong in carrot cake LOL!!) but there is crushed, well drained pineapple in it. The pineapple isn't noticeable, it lends more moisture to the cake. It also has shredded coconut in it, which you can grind a little more finely in a food processor if you want, or leave it out. Don't use desiccated coconut (sometimes called macaroon coconut), it's too dry.
edited to add: yes, if your recipe doesn't include things like nuts, raisins, using a bundt pan is fine. Take care to grease it well, so the cake doesn't stick in the grooves.
