It’s a confusing and digressive start. It begins well enough with the named character going somewhere for a specific reason. It then turns into a mechanism for rounding up the character’s life story until this point. As such, it prevents the book from beginning in a way that makes the reader want to continue. Most of know what we’ve been told has already happened ‘off-stage’.
Any attempt to summarise a life in so few words is going to have problems. It risks feeling superficial and rushed. The character has mentioned three different men with insufficient context to understand who they were and what role they filled in her life. Is Bill short for Barney? Or did she know two men that died? What’s happening with Paul? Is he an important character? It’s all potentially quite confusing but how much of it is important? We can’t say because the story hasn’t really begun. There’s no present context – only a past.
At a technical level, there are a few issues with sentence construction. A comma can’t be used to separate distinct sentences. Subordinate clauses have their uses, but they tend to be misused at the start of sentences, For example, ‘Turning down the lane through the woods she gripped . . .’ puts the emphasis on the turn before the character gripping the wheel. It’s not grammatically wrong, but it does ask the reader to focus primarily on the action rather than the character doing it.