You're a nice Lady ladyaimee, have a look at Heaven on the Planet on Lombok, I've been there and it has an intermediate wave at Inside Ekas at its front after walking down 300 + steps there is also a learner's break on the sandy beach.
This will be way less crowded than anything in Bali.
There is also Outside Ekas but that is definitely not an intermediate wave.
Here is a link
http://www.heavenontheplanet.co.nz/I've been there, fly to Bali then to Lombok 30 minute flight. the HOTP people will pick you up at the airport, tariffs and everything are explained.
Some of the surf travel companies also handle bookings. I suggest this would the way to go as they handle vouchers for internal Indo Flights.
It is not an opulent resort, and it is open to different length of stay. there are massages and some black pearl bargaining and a visit to the local village, it is a Muslim village so a long sarong long sleeve top for you and respectful clothes for sir.
some snorkeling and as I said a beginners wave
Other options have a look at Medewi heading west on the south Coast of Bali. Has a rural feel about it.
Final answer September is still in the swell season and head to the shoulder so less size but great surf.
Nusa Lembongan is another option with accommodation from Feral cost next to nothing and the range up to Club Med costs.
Stuff around $30 per person per night is usually acceptable.
Nusa lembongan is tide dependent, and is all coral reef breaks but Playgrounds offers a reasonable intermediate wave at mid size. Nusa Lembongan is more crowded with day trip surfers from Bali but before and after the boats less so.
Temple visits, NL is Hindu and cave house exploring.
You get a ferry to Nusa Lembongan, there are also ferry services for the places you can stay, I think there is still a day ferry from Benoa or a smaller boat from Padangbai.
Again surf travel companies can help and do all the bookings
my choice HOTP.

I've taken up troll hunting just for fun, instead of a rifle I'll just use a pun! 冲浪爷爷