I haven't used BIS and BAS scales in my research, so I will only point out some general considerations.

Correctness of your correlation analyses.: Double-check your data analysis. Maybe you missed a sign somewhere or you didn't encode some scale correctly.

Interpretation of your correlation analyses. Significant correlation isn't that interesting. You should consider its magnitude. Note that the correlation between two measures is bound by the reliability of those measures. You should compare your correlation estimate with the upper bound and ask how much of the potentially available correlation it explains. In theory, the correlation can't exceed $\sqrt{r_a r_b}$, where $r_i$ is the reliability of measure $i$. (Carver and White provide the reliability estimates on page 323.) In practice this can happen due to measurement error and you should consider the confidence interval of your correlation estimate.

Measurement error or Systematic bias? On page 323 Carver and White (1994) write:

In theory, the sensitivity of the BIS and BAS physiological systems should be independent. Consistent with this assumption, the BIS scale was relatively independent of the BAS subscales in this sample, although the degree of independence varied across subscales. The BIS scale correlated -.12 with Drive, .28 with Reward Responsiveness, and -.08 with Fun Seeking.

You should compare these values with your correlation estimates and ask whether your estimates are consistent with those of Carver and White. Again, confidence intervals may be helpful.

Regression with correlated predictors. Wikipedia explains why linear regression requires independent predictors and has (under Lack of multicolinearity) some suggestions for situations when independence can't be assumed. In addation you may want to look at this question on cross validated SE.

I haven't used BIS and BAS scales in my research, so I will only point out some general considerations.

Correctness of your correlation analyses.: Double-check your data analysis. Maybe you missed a sign somewhere or you didn't encode some scale correctly.

Interpretation of your correlation analyses. Significant correlation isn't that interesting. You should consider its magnitude. Note that the correlation between two measures is bound by the reliability of those measures. You should compare your correlation estimate with the upper bound and ask how much of the potentially available correlation it explains. In theory, the correlation can't exceed $\sqrt{r_a r_b}$, where $r_i$ is the reliability of measure $i$. (Carver and White provide the reliability estimates on page 323.) In practice this can happen due to measurement error and you should consider the confidence interval of your correlation estimate.

Measurement error or Systematic bias? On page 323 Carver and White (1994) write:

In theory, the sensitivity of the BIS and BAS physiological systems should be independent. Consistent with this assumption, the BIS scale was relatively independent of the BAS subscales in this sample, although the degree of independence varied across subscales. The BIS scale correlated -.12 with Drive, .28 with Reward Responsiveness, and -.08 with Fun Seeking.

You should compare these values with your correlation estimates and ask whether your estimates are consistent with those of Carver and White. Again, confidence intervals may be helpful.

Regression with correlated predictors. Wikipedia explains why linear regression requires independent predictors and has (under Lack of multicolinearity) some suggestions for situations when independence can't be assumed. In addation you may want to look at this question on cross validated SE.