Thanks for the info. I would love to be able to afford to take lessons, but that's not in the cards for me. I am starting to wonder if it is even worth trying to learn without help because the first piece of advice I get from everyone is find a good teacher....
The only good teacher in my area is way above my price range.
OK don't get discouraged. Don't quit before you get started. These good folks at DBF have offered heart-felt advice that is hard to argue with and is in the long run right - but you don't HAVE to do it exactly that way. You may have learned to play BG all by your self and you could start in on DB with a little or no help. Much depends on what kind of music you want to play.
But a little help would be good. Get someone that has taken lessons (or played the style music you want) to show you some DB basics - just an hour or so can help get started properly. Or maybe talk to that teacher about taking a couple session on his bass, then decide no or yes and go look for a bass.
Your original question about are you playing it right - probably not. For example you are likely reaching across the neck with your right hand and plucking with finger tips BG style. For DB, generally point your fingers toward the floor and use as much surface of your pointer finger as possible to brush/pull the string. Use wrist motion. This it will seem clumsy and slow at first but it gets the volume up and gets rid of the twang. Now before I get flamed, some do play across the strings, I'm just saying . . .
DB are much quieter that 250 watt stacks so get adjusted to it - really - you may like it. The store bass you were playing may be very sub-par - you just have to get out to hear others and see for yourself. It is not all about plywood vs. carved. I have played old plywood Kays that were LOUD! - seemed twice as loud as mine (also plywood).

They are all different and setup matters. And being the bass player seems to be the worst position possible to hear the bass - 20' out is much better.
Some of the styles you mentioned probably would be amplified DB and really don't require advanced DB techniques . Just take some time to do some research. It is all between you, your music, and your instrument and nothing else. These big old boys do grow on you.
Hope this helps.
