Reference request: Vector bundles and line bundles etc.

I am interested in learning algebraic geometry and I talked to one of my professors today (who is, in part, an algebraic geometer) and he recommended I understand the analytic analogue of the ideas in algebraic geometry so it's not just abstract nonsense when I first see it. Some of specific words he mentioned were vector bundles and line bundles but he could not give any recommendations on the spot and recommended that I ask here.

There are only two sources that I know of which cover these subjects in a way that I think coincide with my relatively modest understanding of mathematics (which I will cover a bit later) are the first part of Hatcher's book on K-theory and Spivak's Comprehensive Introduction to Differential Geometry although the latter will, admittedly, cover much more than I need or could handle at the moment. If there are any more differential geometry concepts of which I should be aware as well, please feel free to include that as well. I am also aware that I will need to know some commutative algebra and complex analysis and I have gotten some solid recommendations on those topics (some from here, in fact).

These are the courses I've taken which I think are relevant to recommendations (all courses are undergraduate): algebra, analysis 1/advanced calculus, differential geometry, proof-based linear algebra, and I am familiar with some topology (in that I know what a topological space is and what a fundamental group is. I will definitely study that more over the summer), I did a reading course on algebraic curves covering the first three chapters of Fulton plus the proof of Bézout's theorem, and I have done an almost reading course in geometry/topology so I am aware of what manifolds are and some of the relevant topology.

Bott and Tu's Differential Forms in Algebraic Topology. (This has a lot of other stuff too, but it's all stuff that you'll need analogues of in algebraic geometry.)

Milnor and Stasheff's book "Characteristic Classes" has a lot of foundational material on vector bundles.