Firstly - it's old-fashioned, and (to me) deliberately confusing. But - to rephrase: when [I was] about to be launched into all the difficulties and dangers of a six weeks’ residence in Bath, it may be stated, for the reader’s more certain information, {unless} the following pages should otherwise fail {to give} any idea of what her character is meant to be, that her heart was affectionate; What it essentially means is 'When I was going to go live in Bath for 6 weeks, I could say that she liked me. or rearranged, with more detail: When I was about to go and live in Bath for 6 weeks, there were potential difficulties and dangers. At that time I could say that her heart was affectionate. I need to say that to tell you, the reader that fact, in case you can't work out what she is like for yourself, based on what you will read in the next few pages.