About 18 months ago, we used Coles & Sons, based in Banbury, Oxfordshire. They brought across my Yamaha XV1700 cruiser from Camberley, Surrey, to Formentera del Segura. Their usual charge is £500, but because it was part of a full house move, they discounted to £350. Two alternative quotes I got were £500 and £600 respectively. It's a family business and we found them to be very helpful and friendly, with good, efficient comms and nothing missing or damaged on arrival here. The office number is 01295 275074, or you can call Dan Coles on his mobile, 07900 892360. They also have a Facebook page:
https://www.facebook.com/ColesandSons/On a related matter, are you planning to use your bike permanently over here, or just for holiday visits? If so, is it a UK spec? I bought my bike from new in the UK, but it was a US import with an extra letter on the registration document, so having paid to get it across to Spain, I couldn't re-register it and ended up selling it! May not be relevant to you, but thought I'd flag it up just in case.