Electrical – Fuse on Primary Side of Transformer keeps blowing

A 50VA transformer will take about 0.21 Amps when correctly loaded (VA / Input voltage)

So a fuse of about 1.5 x the input is suggested and should be Anti Surge (Usually marked T or TT - T stands for "träge" which is german for Lazy or slow) - so 315mA A/S or 400mA A/S

If your fuses are vaporized and cover insides with remains of the wire - This indicates a major short...

What type of transformer are you using - is it a toroidal - if so have you got a shorted turn (if you mount a toroidal transformer incorrectly you can add an extra winding which is shorted out - this is creates by mounting the transformer with a conductive clamp which is bolted down in the middle - if you are using a toroidal - try removing the clamp...)

It is possible that you have a faulty diode in your bridge - I have seen diodes that measure OK when tested with a meter, but when either loaded, or subjected to a higher voltage, break down and become shorts, or leak - the easiest way to prove is to replace ALL the diodes, as I have found if one is faulty, it usually subjects others in the bridge to stress, which may make them more likely fail, and for the cost of 4 diodes of 1N400X or 1N540X - I usually use 1N4007 or 1N5408...

DC motor current ratings are occasionally specified as their no-load current draw.

I would assume that the motor will draw considerably more power when it's starting, or if it's heavily loaded.

What kind of fuse is it blowing? If it's a fast-blow fuse, I would expect it to fail every time the motor starts.