Head to head is 2 for Cibulkova and 3 for Bartoli, although you may say it's 2-2 as their last match in 2011 was cancelled. The other 4 matches were held way back 2008, although those were all on hard court I don't think that would matter as it's way in the past and both have improved since then.
One good thing to note is that in this Carlsbad tournament, Cibulkova's 3 matches were all finished in 2 sets; on the other hand, Bartoli needed 3 sets in all matches.
Marion Bartoli is also having issues with her service game as she committed a total of 29 double faults in his first 2 matches here as compared to Cibulkova's 17 in 3 matches. Against Cibulkova, she can't have those mistakes as Cibulkova's break point conversion is 68.18% (15/22).