If you want a viewfinder and more telephoto, and not a DSLR, the most choices are in the superzoom category. They are also referred to as megazooms, or bridge cameras. Just about every manufacturer makes one. Canon, Nikon, Panasonic, and Sony are the most common, offering anywhere from 24x to 50x zoom lenses. My personal pick would be the Panasonic FZ200, which has the brightest lens, meaning you can take photos in lower light even at full telephoto without losing image quality. Still, these type of cameras work best in daylight, because their sensor are as small as the one in your Pentax camera. I'd probably say the Canon SX50 HS is the next best choice. It has a lot more telephoto with its 50x, 1200mm telephoto equivalent lens. But its aperture is much smaller at telephoto than the Panasonic, so it's strictly a daylight only camera for long zoom photos.
A DSLR is a completely different class of camera. It will of course offer the highest image quality; much better than a superzoom. But if you only print small or view your images to fit your computer screen, you don't necessarily need that extra quality. I don't know how much the D3100 package you found is, but if you go that route, be sure to get a lens to cover the wide angle too unless you will use the Nikon for telephoto only and use your Pentax for wide angle shooting. Personally, I would get a factory refurbished camera; you get the same camera for (usually) less money.
I have a Pentax Optio M20, which is o.k. for general usage, but I would like to get a camera with a viewfinder. I'd also like something better than the 3x zoom for close-ups of the birds in my garden. I have been looking at the Nikon D3100 with a separate 55-300 telephoto lens. Is there anything less expensive which might suffice?