Given your question was around how to improve your search rankings chances I’m going to focus on that. Also, since I’ve not seen your site, I’m going to write as if you have not started your website, so you can just pick and choose what’s already done and where you need to focus. Lastly, will keep this basic, since for now I think you should be able to improve your current efforts and can spend more time learning and making it better later on.
First things first, starting an SEO campaign without a good website or site structure makes things very difficult, so this is where I would start. Here is also where keyword research comes into play. Once you’ve decided the keywords you want to target you should workout exactly what you want to target for each keyword. This is also the time you find out if a keyword is worth targeting. For some sites I've literally spent a few weeks on this so don't worry if this takes a while.
You then need to work on ensuring these pages are optimised for the keyword (e.g. incorporating the keyword into Title, page content, images, ALT, Meta). Add your contact address too, to header or footer. This will help chances of appearing in Local SEO results too. There are some separate steps for this but for now keeping this post focused on what you want to improve.
With a well optimised website, you can start thinking about the links coming to that page and people talking about it to increase chances of Google trusting that page. That’s a big factor. The better the website linking back to you the better it is for you. That’s the general beginners rule. You should also strategically think about adding a few internal links to that page e.g. from blog posts. Since it’s a local business e.g. in Bournemouth think about reaching out to local newspapers/magazines/influencers and getting some press and links to your site. Maybe through an interview or some good work, that’s where the creativity comes in.
I would actually start connecting locally through social media, where you can make some really good connections which should help and even make sure you talk about your brand online to grow it’s overall presence. Nowadays it’s better to grow a system of traffic sources so growing your social presence is a very good way, but that’s for another day
In Summary
1. Start with creating an awesome website (using keyword research to define a good structure for SEO)
2. Optimise website for user experience and keywords
3. Drive links to that page (internal and external) and blog – get creative
