The name looks very unusual. Perhaps it was recorded wrongly when she married? She did not sign her own name, so any wrong spelling might have been overlooked.
The baptism register for
Christ Church Southwark is digitised on Ancestry.
The problem with searching for baptisms in this parish is that the register for the 1780s is badly damaged. While many of the names are readable, many of the years are not, because they are written at the extreme edges of the pages.
Ancestry have indexed these names
without entering a year. So if you enter a year when searching, you are effectively blocking many of the results.
Instead, you could try
browsing the register from page to page, looking for a
Hannah baptised at the 'right' period with a surname that might have been wrongly written down as
Asfer when she married.
https://www.ancestry.co.uk/search/collections/1624/From the
Browse panel on the right select
Borough: Southwark
Parish: Christchurch
Year: 1770-1789
As an anchor-point for this search, baptisms at the turn of the year
1783/1784 are on
image 56 (of 90).
You may not find her, but at least you will know that you have covered that parish properly.