BsonSerializer.RegisterSerializer(new DateTimeOffsetSerializer(BsonType.Document));   

public class MyDateTimeOffsetSerializer : StructSerializerBase<DateTimeOffset>
    {
        public override void Serialize(BsonSerializationContext context, BsonSerializationArgs args,
            DateTimeOffset value)
        {
            IBsonWriter writer = context.Writer;
            writer.WriteString(ToString(value));
        }        
public static string ToString(DateTimeOffset value)
        {
            var x = value.ToString("O");
            return x; // returns string like "2018-07-18T14:35:27.7108283+02:00"
        }        
    }