How can I pivot an average in mysql - mysql

Question

I am trying to display all months where I have bookings, and an running average for bookings/customer for each month, but can't seem to understand how this is achieved and I don't understand why my query is erroring.
I tried several approaches, one of which is the approach of combining two queries, the other is writing it all in one query
The first query returns all months where we have orders:
SELECT date_format(Orders.ServiceDate, '%y-%b') from Orders
GROUP BY YEAR(Orders.ServiceDate), month(Orders.ServiceDate)
The second query is calculating an average of bookings for per customers up until a month:
(
SELECT AVG(cc.total) + 1 AS 'avg' FROM (
SELECT Orders.Customer_ID as 'c',
COUNT(BookingId) 'total' from Orders
where year(Orders.ServiceDate) <= '2019' and month(Orders.ServiceDate)
<= '01'
GROUP BY Orders.Customer_ID
) cc
)
The last queriy is giving me a single number, which is the average for average bookings per customer up until Jan, 2019, but I need the averages for all the months from the first query.
But I need the year and month to be taken from the first query so I get the average for each month, ending up showing something like:
19-Jan 1.5
19-Feb 2
...
...
I tried joining them without luck, so I hope there is a kind soul who can help me further.
The second thing I tried was to do it without joining to queries like this:
SELECT
date_format(z1.ServiceDate, '%y-%b') as months,
(
SELECT
AVG(cc.total) + 1 AS 'avg'
FROM
(
SELECT
z.Customer_ID,
COUNT(z.BookingId) 'total'
from
Orders z
where
YEAR(z.ServiceDate) <= YEAR(z1.months) AND
MONTH(z.ServiceDate) <= MONTH(z1.months)
GROUP BY
z.Customer_ID
) cc
)
from
Orders z1
GROUP BY
YEAR(z1.ServiceDate),
MONTH(z1.ServiceDate)
Here is my schema:
CREATE TABLE IF NOT EXISTS `orders` (
`BookingId` INT(6) NOT NULL,
`ServiceDate` DATETIME NOT NULL,
`Customer_ID` varchar(1) NOT NULL,
PRIMARY KEY (`BookingId`)
) DEFAULT CHARSET=utf8;
INSERT INTO `orders` (`BookingId`, `ServiceDate`, `Customer_ID`) VALUES
('1', '2019-01-03T12:00:00', '1'),
('2', '2019-01-04T12:00:00', '2'),
('3', '2019-01-12T12:00:00', '2'),
('4', '2019-02-03T12:00:00', '1'),
('5', '2019-02-04T12:00:00', '2'),
('6', '2019-02-012T12:00:00', '3');
I was expecting to see two averages, one where we only include up until Jan, and one where feb is included, but I keep getting the error:
"Unknown column 'z1.months' in 'where clause".
How can I make this query work?