Isso fez o truque:
BsonClassMap.RegisterClassMap<Competitor>(cm =>
{
cm.AutoMap();
cm.MapField("_competitorBests").SetElementName("CompetitorBests");
});
BsonClassMap.RegisterClassMap<Competitor>(cm =>
{
cm.AutoMap();
cm.MapField("_competitorBests").SetElementName("CompetitorBests");
});