Given other answers, different native speakers have different perceptions. I'm surprised to discover this. To me (native speaker from France), both the mood and the use of bien make a difference.
“Il semblerait” puts more distanciation in the claim than “il semble”. The indicative mood “il semble” is the speaker's own perception, whereas the conditional mood “il semblerait” is at least notionally conditional to something, generally an implicit or explicit ”according to [someone else]“ or “based on [some observation]”. If there is an explicit reference for the claim, this may strengthen it in that it makes it more trustworthy. But even with an explicit reference, the use of the conditional mood makes the speaker's statement less strong, more open to being wrong. All else being equal, “il semblerait” is somewhat less likely than ”il semble“.
In principle, using “bien” indicates that the sentence comes as a confirmation of some previously stated claim. This indirectly makes the claim more likely since there is more than one piece of evidence for it. “Il semble(rait) bien” is also often used on its own, without confirming anything, and in that case “bien” has a purely emphatic role which does make the claim somewhat more likely.
Between “il semble” and “il semblerait bien”, I don't have a clear scale of likelihood.