DSS tenant, s21 notice, rolling tenancy

Possession - Section 8 and Section 21

I have read through various threads on this throughout the forum and I was wondering if someone could confirm or correct my understanding so far on the above.

I took on a tenant just over 18 months ago on a 6 month contract (RLA tenancy agreement). She was on housing benefit which was paid direct to her, which she then paid into my bank account 24 hours or so later. This was all fine until recently she has been getting later and later with her rent, until this month she has spent the money on other things, and then emailed me to tell me she didnt have her DSS money for the rent this month.

I delivered and got her to sign a s21 b notice at the beginning of the tenancy which she signed and dated.

We have been on a rolling tenancy since her 6 months expired 12 months ago.

Her parting comment to me on the recent email was "feel free to evict me as I will get a council house quicker"

My basic question is, because I have submitted and got a signed s21 b , how quickly can I get her out.

Do i need to still give 2 months notice as required by my tenancy, or does the s21 b change things?

Thanks very much in advance

Hugh