Most Protestant translations, with a few exceptions, are not unreasonably biased theologically. I wouldn't consider them strictly forbidden and a lot of them have more desirable characteristics than common Catholic translations. But this is not really answering your question because you referred to bibles.
The first problem with Protestant bibles is that they are incomplete (nearly all of them) in that they lack the deuterocanonical books that we accept.
The second problem is notes — Protestant explanatory footnotes are going to have a Protestant theological bias. This you can do without (although some popular Catholic explanatory footnotes have their own problems).
A good synthesis translation is the Revised Standard Version - Second Catholic Edition (which is not called that anymore). It's called the Ignatius Bible. This is based on a translation was done by Protestant scholars, and later revised to reflect Catholic sensibilities. This comes in a version, the Ignatius Catholic Study Bible, that has excellent explanatory footnotes. This translation however will require more study and background and may not be suitable for those who aren't interested in serious study.
In particular, it tends, in the interests of fidelity, to strictly retain features and concepts of the original language that may be unfamiliar to the average reader, rather than communicating an equivalent idea or paraphrasing the text in a way a modern reader would easily understand, but at the expense of fidelity and objectivity.
- Maybe you can give us the bible you are looking at (if you're looking at a specific one) and we can give our opinion?
Ultimately, the best translation is the one you will read, however, if the style gets in the way, find another.
There are often Catholic versions of popular Protestant translations so I'd look for those.