for most people, it's not easy... it's certainly not easy for me...
I sing about 1/3 of my band's songs and backing vocals on nearly all the rest and it's mostly a case of knowing the bass lines really well & knowing the vocals really well, and then
not thinking too much about either, whilst you're doing it
if you come to a really tricky bit, trying slowing it RIGHT DOWN and doing them together... usually the hardest bits are when your vocal is doing 1 rhythm and the bass is doing another... I find it helps to discover all the bits they join up, and all the bits where they diverge... work out where the bass plays a note at the same time the vocal has a note, and then 'poke through' the other bass notes around the gaps in the vocal...
sorry, that's probably a really poor way of explaining it...

I'm trying to put into words what I kinda do naturally.. hope you get what I'm trying to get across
practice practice practice... you do get better at it the more you do it... and it's about 10x more fun doing both together than just doing 1 or the other, if you can pull it off
finally - no-one will shoot you if your vocal or bass line isn't exactly like the record... if you need to simplify half a bar or whatever of bass so you can sing over it, then do it
oh, and start with some simple songs... if you try to sing and play Rush stuff right at first, it's asking for trouble.. try really easy stuff so you can get used to hearing your bass rumbling away whilst you're singing

one hard thing at first is NOT singing your bass notes by mistake
