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How expensive is expensive? Higher price obvisouly will get you closer to what you want.
Here is what I found, although I don't think it will be perfect: Genius SP-HF1800A 50W $56.99
The Customer Reviews would have me second guessing. One of them said the packaging left a cone damaged, but thats what the return policy is for although it will lead to headaches. Another one said it has bass, just gets muddy at high volumes. For PC speakers these are sacrafices you will make.
This Speaker has a couple things you were looking for. Its a 2.0 speaker so it should be easy to move. However, it is going to be tall. Not sure how portable you wanted it. It has unprotected cones, so if you do move them often there is a risk of damage. It has its own subwoofer in a 2 speaker factor so it can get bass that a 2.0 speaker usually cannot. It has 20hz to 20khz audio range which is the full human hearing range. Not the absolute best, but getting the best means alot higher price tag. Its a 50 watt speaker meaning it can get some volume to it. Not huge but there. Its also under $100.
I don't know how portable it needs to be to no longer be an issue. To address the Bass issue, your really going to have to just look at a separate sub, and that detracts from portability.
You ~could~ just add a separate subwoofer, if you just want better bass response. They range from $ to $$$+. I wouldn't really recommend this if your existing speakers are quite crap though - you'd get a lot of bass, and still a lot of crappy mids and highs.
The ultimate in portability would either be a headset/headphones (rather than speakers), or something like a Bluetooth soundbox, where you could just pick it up and go. Those won't really give you a lot of bass though.
Hard to go wrong with the classic Klipsh ProMedia 2.1. I've heard the Corsair 2500 is in the same league with regard to sound quality, at about the same price - as I'm not sure the ProMedia 2.1 is still available new everywhere. I wouldn't exactly call either set "portable", but as far as computer setups go, it isn't going to get much easier than that without sacrificing a lot of sound quality that you do going to either headphones or a wireless/bluetooth-type setup.
The next step up, and maybe just as portable, would be to get a small amplifier/receiver, and a set of nice bookshelf speakers. Your budget largely dictates the quality. Yes, you have another box on your desk, but it's multi-purpose, expandable, and can be used for more than just your computer. You can also get ~much~ better sound quality out of this, even better than "Computer" speakers costing several hundred dollars more. This doesn't necessarily need to be expensive - ~$100 can by a really nice setup (Dayton Speakers ($25/set) with a nice little 25W amp - a total setup similar to this: Inexpensive Starter Audiophile system, for example)