"barriers to doing" is correct and can be used in written English.
It generally refers to any obstacles that may be impeding progress. For example, "The lack of resources created numerous barriers to doing the job efficiently."
The barriers to doing business with Russia have also remained stubbornly high.
Both men emphasized that they would not forcibly remove people, pointing out that there are legal barriers to doing so.
And the barriers to doing business are formidable, from bureaucracy and graft to port delays and murky land rights.
However, there are substantial barriers to doing business across international borders — including differences in customs and duty regimes and tax laws.
They could do even better by commercially developing the resources that they have but there are cultural barriers to doing that.
While we have largely (but not entirely) conquered the technological requirements this challenge presents, the commercial and political barriers to doing so are much more daunting.
In a statement released by the White House, Barack Obama said Boggs learned early that "the world needed changing, and she overcame barriers to do just that".
New railway undertakings willing to access these markets have no significant barriers to do so.
Let us fight to free the world, to do away with national barriers, to do away with greed, with hate and intolerance.
Which is why I decided to clamber awkwardly and publically over those invisible, sliding social barriers to do that most uncommon and unrecommended thing: ask.
For instance, even those that use healthcare services may have had to overcome substantial barriers to do so, and conversely, lack of use does not necessarily mean patients had poor access.
