It really depends on your confidence level. It’s a glib answer but, if you’re asking, yes- you ought to use a pro.
Siting a bridge is another critical aspect. Apologies if this is stuff you already know, but just in case others look in…
Any fretted instrument only works if the scale length is right. The distance from the nut to the bridge is the scale length, and the 12th fret is halfway between. If not, the intonation flies out the window and the instrument is almost unuseable. Because strings are non-ideal (and frets are even less so), string saddles can be adjusted to compensate. Generally, you’ll see that the E,A,D saddles are closer to the back of the instrument than the GBE saddles.
Replacing a bridge means placing it in the right spot, because there’s only a certain amount of play with saddle-adjustment. A Bigsby trem is really adding to the complexity. I wouldn’t want to do it myself, but if you know what to do then there’s no law against it.