You may find the jump from Spades to Contract Bridge much larger than you expect. However the popularity of (generic) Bridge pre-dates the invention of Contract Bridge by Harold Stirling Vanderbilt in 1925. If you have a gaming group interested in advancing their card-play skills together, you might consider jumping first to one of the antecedent games from the turn of the Twentieth century, the games that initially inspired early stars such as Sam Stayman and Oswald Jacoby. In chronological order (and thus also in order of increasing complexity):
as well as a more recent related game:
Although the Laws of Contract Bridge are straightforward, at least until you have to deal with irregularities, that is not the source of the game's complexity. Many great minds have worked over the past century developing increasingly complex bidding systems and conventions, and one must know at least one of these in substantial detail before setting foot in Bridge Club or Tournament with intent to play.
However, when your group decides to jump into Contract Bridge, you could do substantially worse than to use an old reference by either Ely Culbertson or Charles Goren. Both of them were extremely accomplished players from the early days of Contract Bridge, and rote extensively to popularize the game. Both advocated a natural bidding style with similar features, the main difference being the use of the more accurate Work Point Count by Goren to replace Culbertson's Quick Trick hand assessment. Old copies of their books are still available at used book stores now and then at very reasonable prices.
Many national and other bridge organizations also publish guides on How to Play Bridge: