First, a speedy method presented by melodeon.net member diatonix:
He uses two pre-cut strips of tape as templates so all tapes are the same length -- one for the short side, and one for the long side. This is quicker and more accurate than measuring each tape individually before cutting. The adhesive is Bindflex 1161, a bookbinding product marketed in Sweden. It is sufficiently tacky to mate the surfaces, and has a relatively long open time. At the end, a small piece of card is used to square up wonky edges, so the finished product is neat and trim.
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The next video is from Lester Bailey. Lester plays, tunes, repairs, and refurbishes melodeons from his workshop in Wendover, Buckinghamshire. You can find his website with contact info in the link, and his details are also in the right-hand sidebar to this page under "Sales & Service Europe+World."
Lester works in an easier way. I emphasize the end result is the same: all tapes cut to uniform length, the job done neatly and professionally. Instead of using a template to cut tapes, he has two rulers on his work surface. Note his advice: if you're using ribbed tape, make sure the ribbing faces the correct direction before gluing.
I use Aleene's Fast Grab Tacky Glue. The 'fast grab' helps the tape stick to the bellows while you fold. You can buy it at most craft stores in the US and it costs about as much as a burrito. It's water soluble and good to have a damp cloth nearby for cleanup.
The devil is in the details, so work quickly and carefully with a mind toward what you're trying to achieve and you should have no problems retaping your bellows.
If you'd like to purchase new bellows tape in the UK, try ordering from Charlie Marshall of CGM Musical. In the United States, try House of Musical Traditions (although CGM will also ship worldwide). I ordered from HMT and they didn't have my color in stock, so I switched the order to black and it arrived two days later. Good luck.