次のコードがそれを行います(C#MongoDB.Driver 2.0)
var collection = database.GetCollection<BsonDocument>("product");
var filter = new BsonDocument();
var update = Builders<BsonDocument>.Update.Inc("UseCount", 1);
var sort = new FindOneAndUpdateOptions<BsonDocument>
{
Sort = Builders<BsonDocument>.Sort.Ascending("UseCount")
};
await collection.FindOneAndUpdateAsync(filter, update, sort);