I would not suggest Magnesium. I am a Mechanical Design Engineer, with a strong back ground in materials.

Mg = Magnesium; Al = Aluminum; St = steel; including Cro-Mo; Ti = Titanium

density (mass per unit volume): Mg 1.8; Al 2.7; Ti 4.5; St 7.8
stiffness (force for a given deflection): Mg 44 GPa; Al 69 GPa; Ti 100 GPa; St 205 GPa
yield strength: Mg 70 MPa; Al 6061 T6 276 MPa; Ti-3Al-2.5V 500 MPa; St 4130 435 MPa

reference: http://www.matweb.com

In practical terms; you can easily permanently bend magnesium with your fingers; it needs to be protected from high pressure loading. For example, if you made handle bars the same size and thickness has standard aluminum handle bars; you could easily leave permanent and deep impressions just by squeezing it with your hands; and the first heavy braking would result in severely bent if not broken bars. As noted, magnesium has some corrosion issues; but they are not significantly different from aluminum.

Magnesium is used for some notebook computers, where its ability to be cast into very intricate shapes provides enough of an advantage to make sense.

For fabricate a traditional style bicycle (joined tubing); magnesium does not make sense. If were to cast or mold the frame in one piece, magnesium MIGHT be worth another look.