Hi Lesley,
I understand how daunting it must be travelling by yourself so I have had a look into parking etc for you.....
It will take you approx 2.5 hours to travel to Gatwick from Bristol. I understand you are stopping over the night before departure, which gives you a little more time to get your head together. When you arrive at the airport, there should be a sign for 'holiday airport parking'. Take a ticket and follow the signs for 'arrivals'. After parking, just head to reception, where you hand over your keys in return for a receipt(keep this safe). When you return from your holiday, return the receipt to reception and your keys will be handed back to you safe and sound.
This secure carpark is located about 2 miles from the airports North terminal so there is shuttle bus that runs every half an hour to the main airport which takes about 7-9 minutes. I have priced up for an average 8 day stay and it comes out at between £60-£65.
I hope this helps!
Cheryl, your editor