That's pretty much it Adrian. When you claim the 45p you should buy your fuel out of your personal bank account not your business account and leave it out of ClearBooks. You can then enter each business trip in ClearBooks using the mileage tool, and once a month (or weekly if you prefer, up to you) approve all the trips to create a single expense claim which appears in CB as an invoice payable to yourself. Pay that, like you would any other supplier's invoice, by transferring the amount from your business to your personal bank account. As you say, the 45p is simple to claim, and it also avoids any argy-bargy with HMRC over the validity of deductions for personal use. By claiming each business trip in CB you have a pretty bullet-proof record to support the deduction from taxable profits.
Just one other thing to note, if you're VAT registered you still need to keep some fuel receipts to support your claim for recovery of some VAT on the 45p paid to you. You just file the receipts though, don't enter them in CLearBooks. If not VAT registered you can just forget all that, no need to keep any invoices/bills for motoring costs if you claim the 45p.